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1. JSTOR Further Consistency And Independence Results In NF Obtained THE JOURNAL OF SYMBOLIC LOGIC Volume 48, Number 2, June 1983 FURTHER Consistency and independence results IN NF OBTAINED BY THE PERMUTATION METHOD T. E. http://links.jstor.org/sici?sici=0022-4812(198306)48:2<236:FCAIRI>2.0.CO;2-V

2. Further Consistency And Independence Results In NF Obtained By The Further Consistency and independence results in NF Obtained by the Permutation Method. T. E. Forster. Source J. Symbolic Logic Volume 48, Issue 2 (1983), http://projecteuclid.org/handle/euclid.jsl/1183741241

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Further Consistency and Independence Results in NF Obtained by the Permutation Method T. E. Forster Source: J. Symbolic Logic Volume 48, Issue 2 (1983), 236-238. Full-text: Remote access If you are a member of the ASL, log in to Euclid for access. Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR. Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.jsl/1183741241 JSTOR: links.jstor.org back to Table of Contents previous next Journal of Symbolic Logic Current Issue All Issues Search this Journal Editorial Board ... Log in RSS Cornell University Library

3. Date Wed, 24 Mar 1999 111812 -0700 From Randall Holmes Holmes So the practice of studying Consistency and independence results makes perfect sense from the secondorder ZFC standpoint; the only difference is one of http://math.boisestate.edu/~holmes/holmes/fomletter15.txt

Date: Wed, 24 Mar 1999 11:18:12 -0700 From: Randall Holmes

4. Hilbert's First And Second Problems And The Foundations Of Mathematics By Peter Part B, on set theory, has many Consistency and independence results, including applications to topology. The article by J.P. Burgess in Part B gives a fine http://at.yorku.ca/t/a/i/c/52.htm

Topology Atlas Document # taic-52 Topology Atlas Invited Contributions vol. 9, no. 3 (2004) 6 pp. Hilbert's first and second problems and the foundations of mathematics Peter J. Nyikos Department of Mathematics University of South Carolina Columbia, SC 29208 USA http://www.math.sc.edu/~nyikos AtlasImage format 6 pages PostScript file (113 Kb) Adobe PDF file (126 Kb) DVI file (21 Kb) LaTeX file (16 Kb) In 1900, David Hilbert gave a seminal lecture in which he spoke about a list of unsolved problems in mathematics that he deemed to be of outstanding importance. The first of these was Cantor's continuum problem, which has to do with infinite numbers with which Cantor revolutionised set theory. The smallest infinite number, , `aleph-nought,' gives the number of positive whole numbers. A set is of this cardinality if it is possible to list its members in an arrangement such that each one is encountered after a finite number (however large) of steps. Cantor's revolutionary discovery was that the points on a line cannot be so listed, and so the number of points on a line is a strictly higher infinite number ( c , `the cardinality of the continuum') than . Hilbert's First Problem asks whether any infinite subset of the real line is of one of these two cardinalities. The axiom that this is indeed the case is known as the Continuum Hypothesis ( CH This problem had unexpected connections with Hilbert's Second Problem (and even with the Tenth, see the article by M. Davis and the comments on the book edited by F. Browder). The Second Problem asked for a proof of the consistency of the foundations of mathematics. Some of the flavor of the urgency of that problem is provided by the following passage from an article by S.G. Simpson in the same volume of JSL as the article by P. Maddy:

5. The Consistency Of "P = NP" And Related Problems With Fragments Of Number Theory Consistency results represent an approach to the lower bound problems of complexity 4 J. Hartmanis and J. Hopcroft, “independence results in Computer http://portal.acm.org/citation.cfm?id=800141.804652

6. Interests Ever since 1977, I have been a leading researcher in the part of topology that deals with these Consistency and independence results. http://www.math.sc.edu/~nyikos/statement.html

Statement of research interests: I am especially active in that part of topology which is involved with set-theoretic consistency and independence of some very basic topological concepts. This is part of what I call the legacy of Kurt Goedel, who first showed that there are mathematical statements whose truth or falsity cannot be decided on the basis of the axioms on which all of mathematics up to Goedel's day was based. Although over sixty years have passed since then, no one has come up with any new axioms that are generally seen to be true. However, in the meantime, a multitude of statements in mathematics, including some in almost every one of the main areas of pure mathematics, have been shown to be undecidable on the basis of the generally accepted axioms. Many of them are easy to state, in fact easier to state and more fundamental to some branches of mathematics, than most of the true statements that are being proven in these branches today. Topology is one branch that has been completely revolutionized in the past three decades as a result. Ever since 1977, I have been a leading researcher in the part of topology that deals with these consistency and independence results. To take just one example: in 1948, M. Katetov proved that a compact space is metrizable if, and only if, every subspace of its cube is normal; he then asked whether ``cube'' could be replaced by ``square''. In 1977, I showed that it is consistent that the answer is negative, while in 2001, P. Larson and S. Todorcevic showed that it is consistent that the answer is affirmative.

7. Gentzen's Consistency Proof - Wikipedia, The Free Encyclopedia In 1936 Gerhard Gentzen proved the Consistency of firstorder arithmetic using Kirby, L. and Paris, J., Accessible independence results for Peano http://en.wikipedia.org/wiki/Gentzen's_consistency_proof

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Gentzen's consistency proof From Wikipedia, the free encyclopedia Jump to: navigation search This article or section is in need of attention from an expert on the subject. WikiProject Mathematics or the Mathematics Portal may be able to help recruit one. If a more appropriate WikiProject or portal exists, please adjust this template accordingly. edit Gentzen's theorem In 1936 Gerhard Gentzen proved the consistency of first-order arithmetic using combinatorial methods. In itself, the result is rather trivial, since the consistency of first-order arithmetic has a very easy proof: the axioms are true—in a mathematically defined sense—the rules of predicate calculus preserve truth and no contradiction is true, hence no contradiction follows from the axioms of first-order arithmetic. What makes Gentzen's proof interesting is that it shows much more than merely that first-order arithmetic is consistent. Gentzen showed that the consistency of first-order arithmetic is provable, over the weaker base theory of primitive recursive arithmetic with the additional principle of quantifier free transfinite induction up to the ordinal epsilon nought The principle of quantifier free transfinite induction up to ε says that for any formula A(x) with no bound variables transfinite induction up to ε holds. ε

8. 03E: Set Theory However, results in mathematical logic imply it is impossible to determine 03E35 Consistency and independence results; 03E40 Other aspects of forcing http://www.math.niu.edu/~rusin/known-math/index/03EXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 03E: Set theory Introduction Naive set theory considers elementary properties of the union and intersection operators Venn diagrams, the DeMorgan laws, elementary counting techniques such as the inclusion-exclusion principle, partially ordered sets, and so on. This is perhaps as much of set theory as the typical mathematician uses. Indeed, one may "construct" the natural numbers, real numbers, and so on in this framework. However, situations such as Russell's paradox show that some care must be taken to define what, precisely, is a set. However, results in mathematical logic imply it is impossible to determine whether or not these axioms are consistent using only proofs expressed in this language. Assuming they are indeed consistent, there are also statements whose truth or falsity cannot be determined from them. These statements (or their negations!) can be taken as axioms for set theory as well. For example, Cohen's technique of forcing showed that the Axiom of Choice is independent of the other axioms of ZF. (That axiom states that for every collection of nonempty sets, there is a set containing one element from each set in the collection.) This axiom is equivalent to a number of other statements (e.g. Zorn's Lemma) whose assumption allows the proof of surprising even paradoxical results such as the Banach-Tarski sphere decomposition. Thus, some authors are careful to distinguish results which depend on this or other non-ZF axioms; most assume it (that is, they work in ZFC Set Theory).

9. FOM: 103:Hilbert's Program For Consistency Proofs/1 Why doesn t the usual results about Consistency proofs of a system such as . 14 Errata 4/8/98 948AM 15Structural independence results and provable http://cs.nyu.edu/pipermail/fom/2001-April/004868.html

FOM: 103:Hilbert's Program for Consistency Proofs/1 Harvey Friedman friedman at math.ohio-state.edu Wed Apr 11 11:10:15 EDT 2001 Previous message: FOM: IEEE Data Mining 2001: Call for Workshop Proposals Next message: FOM: Foundations of the Formal Sciences (FotFS) III Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: FOM: IEEE Data Mining 2001: Call for Workshop Proposals Next message: FOM: Foundations of the Formal Sciences (FotFS) III Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

10. Two Impossibility Results On The Converse Consistency Principle In Bargaining 1999 Abstract We present two impossibility results on the converse Consistency Pareto optimality, contraction independence, and converse Consistency. http://ideas.repec.org/p/snu/ioerwp/no24.html

This file is part of IDEAS , which uses RePEc data Papers Articles Software Books ... Help! Two Impossibility Results on the Converse Consistency Principle in Bargaining Author info Abstract Publisher info Download info ... Statistics Author Info Youngsub Chun liame2('kr','ac','snu','plaza','m7i7','ychun') Abstract We present two impossibility results on the converse consistency principle in the context of bargaining. First, we show that there is no solution satis-fying Pareto optimality, contraction independence, and converse consistency. Next, we show that there is no solution satisfying Pareto optimality, strong individual rationality, individual monotonicity, and converse consistency. Download Info To download: If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help file . Note that these files are not on the IDEAS site. Please be patient as the files may be large. File URL: http://econ.snu.ac.kr/~ecores/activity/paper/no24.pdf

11. Project: Categorical Logic And Proof Theory: Realizability For Constructive Theo These include relative Consistency and independence results. One example of the former is to prove that the Consistency of constructive set theory implies http://www.onderzoekinformatie.nl/en/oi/nod/onderzoek/OND1297331/

Login English KNAW Research Information NOD - Dutch Research Database ... Research entire www.onderzoekinformatie.nl site fuzzy match Project: Categorical logic and proof theory: realizability for constructive theories Print View Titel Categorische logica en bewijstheorie: realiseerbaarheid voor constructieve theorie«n Abstract Period Status completed Related organisations Financier: NWO Council for Physical Sciences Secretariat: Department of Mathematics (UU) Related persons Project leader: Prof.dr. I. Moerdijk Researcher: Drs. F. de Marchi Classification fundamental research logic, set theory and arithmetic Data supplier: Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) Back NOD page Last modified: 12-07-2005 00:00

12. Graduate Courses Consistency problems. Additional reading on selected topics.TOC . Recent Consistency and independence results (Godel, Cohen).TOC http://www.math.buffalo.edu/gr_course_list.html

Graduate Courses Academics Courses by Areas Web-based Are You Ready quiz/reviews Select a course title to see the course description. When viewing the course description, select [TOC] to return to the table of contents Jump to Top of page 511 Probability Theory (4) (F) 512 Introduction to Statistical Inference (4) (Sp) 513 Introduction to Mathematical Logic I (3) ... 599 Supervised Teaching (1-4) Jump to Top of page 613-614 Mathematical Logic (3, 3) 615-616 Axiomatic Set Theory (3, 3) 619-620 Algebra (3, 3) ... 649-650 Partial Differential Equations (3, 3) Jump to Top of page 713-714 Recursive Functions (3, 3) 715-716 Intuitionistic Mathematics (3, 3) 719-720 Advanced Algebra (3, 3) ... 743-744 Topics in Differential Geometry (3, 3) Jump to Top of page 800 Thesis Guidance (1-12) 801 Reading and Conference (1-6) 805 Colloquium (1-4) ... 840 Seminars in Applied Mathematics (variable) Jump to Top of page 511 Probability Theory (4) (F) Prerequisite: MTH 141 MTH 142 or equivalent Description: A first course in probability. Introduces the basic concepts of probability theory and addresses many concrete problems. A list of basic concepts includes axioms of probability, conditional probability, independence, random variables (continuous and discrete), distribution functions, expectation, variance, joint distribution functions, limit theorems. [TOC] 512 Introduction to Statistical Inference (4) (Sp) :Description: Topics include: review of probability, conditional probability, Bayes' Theorem; random variables and distributions; expectation and properties; covariance, correlation, and conditional expectation; special distributions; Central Limit Theorem and applications; estimations, including Bayes; estimators, maximum likelihood estimators, and their properties. Includes use of sufficient statistics to 'improve' estimators, distribution of estimators, unbiasedness, hypothesis testing, linear statistical models, and statistical inference from the Bayesian point of view.

13. The Journal Of Symbolic Logic, Volume 48 225235 BibTeX T. E. Forster Further Consistency and independence results in NF Obtained by the Permutation Method. 236-238 BibTeX Bruno Poizat Paires http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml48.html

The Journal of Symbolic Logic , Volume 48 Volume 48, Number 1, March 1983 Harrie C. M. de Swart : A Gentzen- or Beth-Type System, a Practical Decision Procedure and a Constructive Completeness Proof for the Counterfactual Logics VC and VCS. 1-20 BibTeX Henry A. Kierstead Jeffrey B. Remmel : Indiscernibles and Decidable Models. 21-32 BibTeX Menachem Magidor Saharon Shelah Jonathan Stavi : On the Standard Part of Nonstandard Models of Set Theory. 33-38 BibTeX G. P. Monro : On Generic Extensions Without the Axiom of Choice. 39-52 BibTeX G. C. Nelson : Logic of Reduced Power Structures. 53-59 BibTeX Bruno Poizat BibTeX Solomon Feferman : Choice Principles, the Bar Rule and Autonomously Iterated Comprehension Schemes in Analysis. 63-70 BibTeX William G. Fleissner : Sone of George and V = L. 71-77 BibTeX A. J. Dodd : Core Models. 78-90 BibTeX Stevo Todorcevic : Real Functions on the Family of All Well-Ordered Subsets of a Partially Ordered Set. 91-96 BibTeX Jean Porte : Antitheses in Systems of Relevant Implication. 97-99 BibTeX Iraj Kalantari Anne Leggett : Maximality in Effective Topology. 100-112 BibTeX Penelope Maddy : Proper Classes. 113-139

14. Emerald: Article Request However, having regard to the range and Consistency of accuracy at the . through Consistency and independence and the achievement of results which do not http://www.emeraldinsight.com/Insight/ViewContentServlet?Filename=Published/Emer

15. 03Exx 03E35 Consistency and independence results; 03E40 Other aspects of forcing and Booleanvalued models; 03E45 Inner models, including constructibility, http://www.ams.org/msc/03Exx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions Prev: Set theory 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory 03E10 Ordinal and cardinal numbers 03E15 Descriptive set theory [See also 03E17 Cardinal characteristics of the continuum 03E20 Other classical set theory (including functions, relations, and set algebra) 03E25 Axiom of choice and related propositions 03E30 Axiomatics of classical set theory and its fragments 03E35 Consistency and independence results 03E40 Other aspects of forcing and Boolean-valued models 03E45 Inner models, including constructibility, ordinal definability, and core models 03E47 Other notions of set-theoretic definability 03E50 Continuum hypothesis and Martin's axiom 03E55 Large cardinals 03E60 Determinacy principles 03E65 Other hypotheses and axioms 03E70 Nonclassical and second-order set theories 03E72 Fuzzy set theory 03E75 Applications of set theory 03E99 None of the above, but in this section

16. Logic Colloquium 2006 These models provide a general tool to prove relative Consistency and independence results, analogous to the classical method of forcing. http://www.cs.ru.nl/lc2006/invited.html

main invited contributed registration how to get there Invited talks This page contains the schedule and abstracts of the tutorials, the plenary talks and the special sessions at the Logic Colloquium 2006 Schedule The following facilities will be available in each room: Beamer Laptop (for people who did not bring their own laptop: possible file formats .pdf .ps .ppt) Overhead projector Black board or white board At your convenience you can send a .pdf file with your slides to Jasper Stein ( jasper@cs.ru.nl ) who will have it pre-installed on the presentation computer. Room 1 Samson Abramsky, Categorical Quantum Logic Room 1 Ieke Moerdijk, Introduction to Algebraic Set Theory (First Part) Room 1 Marat Arslanov, Problems of definability and structural differences among elementary theories of the Ershov difference hierarchy Room 1 (Chair: Ralf Schindler) Natasha Dobrinen, Co-stationarity of the ground model, internal consistency, and new sequences John Krueger, Some Consistency Results Related to Internal Approachability Room 2 (Chair: Michael Rathjen) Klaus Aehlig

17. Piotr Koszmider's Web Page Many of these results are Consistency or independence results. For example, we have conjectures of Kaplansky 1 and of Pelczynski 2. http://www.ime.usp.br/~piotr/cv/ativpas22004e.html

FORCING INFINITY TOPOLOGY BANACH SPACES C(K) Home Contact Recent preprints Publications ... Previous teaching Curiculum Vitae academic activities invited lectures contributed lectures profissional services ... Resources Pages of matematicians Conferences Papers on-line Bulletin Boards Funding sources Institutes Popular resources Previous activities by semester PIOTR KOSZMIDER, ASSOCIATED PROFESSOR, MAT - IME - USP A. J. Heschel Who is man? The Raymond Fred West Memorial Lectures at Stanford University, 1963. ACTIVITIES DURING THE SECOND SEMESTER 2004 RESEARCH PROJECT 2001 - 2006 Applications of Infinitary Combinatorics in Undecidable Problems on Boolean algebras, compact spaces and Banach spaces. Supported by National Reserach Council (Brazil): Produtividade em Pesquisa (B2) fellowship. There is a classical chain of mathematical constructions: infinite families of sets which form Boolean algebras which induce, by the Stone duality compact topological spaces on which we can consider Banach spaces of continuous functions C(K) and Radon measures , the latter is the dual space of the former, we can can even get the operator algebra on the C(K).

18. On The Measurements Of Board Composition: Poor Consistency And A Serious Mismatc This results in a poor fit with a chi^sup 2^ of 494.79 (65 dJ), a CFI of .48, either singly or in concert, constitute a measure of board independence? http://findarticles.com/p/articles/mi_qa3713/is_199901/ai_n8836120/pg_6

@import url(/css/us/pub_page_article.css); @import url(/css/us/template_503.css); @import url(/css/us/tabs_503.css); @import url(/css/us/fa_bnet.css); @import url(http://i.bnet.com/css/fa.css); BNET Research Center Find 10 Million Articles BNET.com Advanced Search Find in free and premium articles free articles only premium articles only this publication Arts Autos Business Health News Reference Sports Technology Explore Publications in: all Arts Autos Business ... Technology Content provided in partnership with FIND IN free and premium articles free articles only premium articles only this publication Arts Autos Business Health News Reference Sports Technology Advanced Search print share ... link On the measurements of board composition: Poor consistency and a serious mismatch of theory and operationalization Decision Sciences Winter 1999 by Daily, Catherine M Johnson, Jonathan L Dalton, Dan R < Page 1 Continued from page 5. Previous Next Next, we considered the within-category fit for outside director proportion items. The CFI (.70) and IFI (.70) are very poor, suggesting that these items do not constitute a construct. By examining item factor loadings, error terms, and R^sup 2^ estimates (see Table 4), those items that contribute to the poor fit of a model can be eliminated. This trimmed model, obtained by eliminating two items (identified as O3 and O4 in Table 2b) results in a robust model with a CFI and IFI of .93, a composite reliability of .95, and a variance extracted estimate of .75. This demonstrates that certain of the outside director metrics do, in concert, constitute a robust construct.

19. Solomon A. Asch : Opinions And Social Pressure (1955) I shall report first the statistical results of a series in which a total of . If Consistency of independence or conformity in behavior is shown to be a http://www.panarchy.org/asch/social.pressure.1955.html

Index Solomon A. Asch Opinions and Social Pressure Note In the 1950s the social psychologist Solomon Asch conducted a famous experiment that highlighted the fragility of the person in a mass society when he is confronted with the contrary opinion of a majority, and the tendency to conform even if this means to go against the person's basic perceptions. This is a chilling text that should be carefully read and remembered whenever we think we are swayed by the mass, against our deepest feelings and convictions. At that moment we should be on the alert, re-examining all positions (our included) and then taking decisions as free, mature and fully responsible human beings, whatever the direction taken by the mass or by a majority. That social influences shape every person's practices, judgments and beliefs is a truism to which anyone will readily assent. A child masters his "native" dialect down to the finest nuances; a member of a tribe of cannibals accepts cannibalism as altogether fitting and proper. All the social sciences take their departure from the observation of the profound effects that groups exert on their members. For psychologists, group pressure upon the minds of individuals raises a host of questions they would like to investigate in detail. How, and to what extent, do social sources constrain people's opinions and attitudes? This question is especially pertinent in our day. The same epoch that has witnessed the unprecedented technical extension of communication has also brought into existence the deliberate manipulation of opinion and the "engineering of consent." There are many good reasons why, as citizens and as scientists, we should be concerned with studying the ways in which human beings form their opinions and the role that social conditions play.

20. The Mathematics Genealogy Project - Paul Szeptycki Dissertation Some Consistency and independence results On Countably Metacompact Spaces. Advisor 1 Franklin Tall Advisor 2 William Weiss. Student(s) http://genealogy.math.ndsu.nodak.edu/id.php?id=16213

21. 03Exx set theory and its fragments 03E35 Consistency and independence results 03E40 Other aspects of forcing and Booleanvalued models 03E45 Inner models, http://www.emis.de/MSC2000/03Exx.html

Set theory 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory 03E10 Ordinal and cardinal numbers 03E15 Descriptive set theory [See also ] 03E17 Cardinal characteristics of the continuum 03E20 Other classical set theory (including functions, relations, and set algebra) 03E25 Axiom of choice and related propositions 03E30 Axiomatics of classical set theory and its fragments 03E35 Consistency and independence results 03E40 Other aspects of forcing and Boolean-valued models 03E45 Inner models, including constructibility, ordinal definability, and core models 03E47 Other notions of set-theoretic definability 03E50 Continuum hypothesis and Martin's axiom 03E55 Large cardinals 03E60 Determinacy principles 03E65 Other hypotheses and axioms 03E70 Nonclassical and second-order set theories 03E72 Fuzzy set theory 03E75 Applications of set theory 03E99 None of the above, but in this section Version of December 15, 1998

22. UH Math Department Analysis Research Group Axiomatic development, ordinal and cardinal numbers, recursion theorems, axiom of choice, continuum hypothesis, Consistency and independence results. http://www.math.hawaii.edu/home/Courses.html

Printable Version Mathematics (MATH) UH version Algebra Courses Analysis Courses Applied Courses Logic Courses Topology Courses Graduate Division Upper Division Lower Division Courses All Courses

23. 03Exx 03E35, Consistency and independence results. 03E40, Other aspects of forcing and Booleanvalued models. 03E45, Inner models, including constructibility, http://www.impan.gov.pl/MSC2000/03Exx.html

Set theory Partition relations Ordered sets and their cofinalities; pcf theory Other combinatorial set theory Ordinal and cardinal numbers Descriptive set theory [See also Cardinal characteristics of the continuum Other classical set theory (including functions, relations, and set algebra) Axiom of choice and related propositions Axiomatics of classical set theory and its fragments Consistency and independence results Other aspects of forcing and Boolean-valued models Inner models, including constructibility, ordinal definability, and core models Other notions of set-theoretic definability Continuum hypothesis and Martin's axiom Large cardinals Determinacy principles Other hypotheses and axioms Nonclassical and second-order set theories Fuzzy set theory Applications of set theory None of the above, but in this section

24. MU Department Of Mathematics, Statistics And Computer Science ordinal and cardinal arithmetic, the continuum hypothesis, methods of inner models and forcing for proving Consistency and independence results. http://www.mscs.mu.edu/mscs/graduate/grd_bulletin.html

MSCS Graduate Studies Graduate Bulletin MSCS Graduate Programs Admission Financial Aid MSCS Graduate Handbook ... print MSCS Graduate Bulletin for 2007-2008 Updated Nov 29, 2007 Chairperson and Professor: Jones Acting Chair and Professor: Merrill Assistant Chairperson: Manyo Professor : Bankston, Bansal, Braunschweiger (Emeritus), Clough, Corliss,Hamedani, Hanneken (Emeritus), Harris, Krenz, Lawrence (Emeritus), Moyer, Pastijn, Ziegler (Emeritus) Associate Professor : Brookshear (Emeritus), Byleen, Ruitenburg, Simms, Slattery Research Associate Professor : Liu, Tonellato Assistant Professor : Ahamed, Bajorunaite, Brylow, J. Factor, K. Factor, Madiraju, Sanders, Scott, Struble NOTE: Faculty members and their ranks are for the 2007-2008 academic year. DEGREES OFFERED: Master of Science, students are admitted under Plan B (non-thesis option) but Plan A (thesis option) is also offered; Doctor of Philosophy SPECIALIZATIONS: Master's: Computer Science, Mathematics, Mathematics Education Doctoral: Algebra, Biomathematics, Logic and Foundations, Statistics Information on the master’s degree program in computing can be found in the Computing section of this bulletin. Similarly, information on the master’s degree program in bioinformatics can be found in the Bioinformatics section.

25. Mathematics - UC Santa Barbara 2007-2008 General Catalog results on the Algebra Diagnostic Test are substantially improved by transfinite constructible sets, Consistency and independence results of Gödel http://www.catalog.ucsb.edu/2008cat/depts/math.htm

Click to Print Department of Mathematics Division of Mathematical, Life, and Physical Sciences South Hall 6607 Telephone: (805) 893-2171 Undergraduate e-mail: ugrad@math.ucsb.edu Graduate e-mail: math-gradinfo@math.ucsb.edu Website: www.math.ucsb.edu (will open in a new browser window) Department Chair: Jeffrey Stopple Contents: Faculty Emeriti Faculty Affiliated Faculty Overview ... Graduate Courses Faculty Adebisi Agboola , Ph.D., Columbia University, Professor (number theory) Charles A. Akemann , Ph.D., UC Berkeley, Professor (functional analysis) Stephen Bigelow , Ph.D., UC Berkeley, Associate Professor (low-dimensional topology) Bjorn Birnir , Ph.D., Courant Institute, Professor (nonlinear partial differential equations) Maria Isabel Bueno Cachadina , Ph.D., Universidad Carlos III de Madrid, Lecturer (numerical linear algebra) Paolo Cascini , Ph.D., Courant Institute, Assisant Professor (algebraic geometry) Hector Ceniceros , Ph.D., Courant Institute, Associate Professor (numerical analysis) Daryl Cooper , Ph.D., University of Warwick, Professor (topology, group theory) Xianzhe Dai , Ph.D., State University of New York, Stony Brook, Professor (Geometric Analysis)

26. LogBlog: April 2006 | Richard Zach | Philosophy | University Of Calgary and b. the unsolvability statements obtained from Consistency and the like have that logical independence results are irrelevant to number theory, http://www.ucalgary.ca/~rzach/logblog/2006_04_01_archive.html

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27. Iowa State University Courses And Programs Survey of Consistency and independence results. Math 584. Category Theory. (30) Cr. 3. Alt. F., offered 1996. Prereq 302. Categories and functors and http://www.iastate.edu/~catalog/9597/math.html

Courses and Programs General Catalog Index 95-97 Catalog Index Schedule of Classes Registrar's Homepage ... Graduate Courses Math (Math) Math 10. High School Algebra. (4-0) Cr. 0. F.S.SS. For students who do not have adequate facility with topics from high school algebra or do not meet the algebra admission requirement. All students should initially enroll in Math 10. The course is divided into tracks of one- and two-semester lengths. For most students a diagnostic exam will determine which track must be taken, while those not meeting the algebra admission requirement must take a two-semester track. Students will receive a grade in Math 25 or 30 respectively depending on the level of material covered. Satisfactory completion of Math 30 is recommended for students planning to take Math 140 or 151, while Math 25 is sufficient for Math 104, 105, 150, 195, Stat 101 or 105. Students must complete Math 30 to remove a deficiency. Topics include signed numbers, polynomials, rational and radical expressions, exponential and logarithmic expressions, and equations. Offered on a satisfactory-fail basis only. Developmental math fee. Math 20. High School Geometry.

28. Mathematics infinitary logic and admissible sets, ordinary and generalized recursion theory, Consistency and independence results in set theory, large cardinals, http://pr.caltech.edu/catalog/05_06/courses/listing/ma.html

The online version of the Caltech Catalog is provided as a convenience; however, the printed version is the only authoritative source of information about course offerings, option requirements, graduation requirements, and other important topics. Mathematics Ma 1 abc. Calculus of One and Several Variables and Linear Algebra. 9 units (4-0-5); first, second, third terms. Prerequisites: high-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7). Review of calculus. Complex numbers, Taylor polyno-mials, infinite series. Comprehensive presentation of linear algebra. Deriva-tives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence. These students will not learn series in Ma 1 a and will be required to take Ma 1 d. Instructors: Simon, Aschbacher, Wales, Ramakrishnan, Dunfield. Ma 1 d. Series.

29. Lower Extremity Function And Subsequent Disability: Consistency Across Studies, Consistency Across Studies, Predictive Models, and Value of Gait Speed Alone Disability results From the Lifestyle Interventions and independence for http://biomed.gerontologyjournals.org/cgi/content/abstract/55/4/M221?ck=nck

30. Logic In Leeds - Postgraduate Opportunities independence results, Finitary Combinatorics and Theories of Program induction needed to prove the theory consistent, i.e. Consistency strength . http://www.maths.leeds.ac.uk/pure/logic/postgrad.html

People Research Seminars Postgrad opportunities Pure Department School of Mathematics University of Leeds Some outside links Graduate courses Homepage Postgraduate Studies Contents Introduction Current Research in the Mathematical Logic Group Funding International Students ... Enquiries Please also see the School of Maths Postgraduate Brochure , which has far more general information, and puts logic in the context of the other research groups. INTRODUCTION The Department of Pure Mathematics forms part of the School of Mathematics, the other departments being those of Applied Mathematical Studies and Statistics. The department has 20 academic staff, as well as a number of postdoctoral research fellows and research assistants. The Department was rated 5 in both of the last two Research Assessment Exercises. There are usually about 30 research students. As well as the weekly seminars which are mentioned below, there is a less specialised departmental Colloquium which meets once or twice a term. There is also a graduate lecture course each year in each of Mathematical Logic, Algebra, Analysis and Differential Geometry. The aim of the Department of Pure Mathematics at Leeds for many years has been to maintain and develop research groups of international standing in four of the most vital and central areas of mathematics: mathematical logic, algebra, analysis and differential geometry. In each of these subjects there is plenty of lively research activity at Leeds. The department is one of the largest and most active centres for pure mathematics research in the UK, and is an ideal place in which to obtain postgraduate training.

31. Peter Clote's Publications Two further combinatorial theorems equivalent to the 1Consistency of Peano . Anti-basis theorems and their relation to independence results in Peano http://clavius.bc.edu/~clote/publications.html

Publications Table of Contents Books Journal Articles Refereed Articles in Books Refereed Articles in Proceedings Books Boolean Functions and Models of Computation , by P. Clote and E. Kranakis, 615 pages, Springer-Verlag, 2003, ISBN: 3-540-59436-1 (hardcover). Computational Molecular Biology: An Introduction Japanese translation of Computational Molecular Biology: An Introduction , P. Clote and R. Backofen (2005). Computer Science Logic , by P. Clote and H. Schwichtenberg (Eds.), 14th International Workshop, CSL 2000, Springer Lecture Notes in Computer Science , ISBN 3-540-67895-6, August 2000. Arithmetic, Proof Theory and Computational Complexity , Oxford University Press, eds. P. Clote and J. Krajicek (1993). Feasible Mathematics II Research monograph translation, Theory of Relations Back to Table of Contents Journal Articles Proteins: Structure, Function and Bioinformatics , to appear. Nucleic Acids Res. , Web Server Issue (2006), in press. DiANNA 1.1: An extension of the DiANNA web server for ternary cysteine classification, F. Ferre, P. Clote, Nucleic Acids Res.

32. The Frege-Hilbert Controversy (Stanford Encyclopedia Of Philosophy) By presenting a rich trove of Consistency and independence demonstrations, Hilbert displays here the power of the “formal” approach to axioms, http://plato.stanford.edu/entries/frege-hilbert/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free The Frege-Hilbert Controversy First published Sun Sep 23, 2007; substantive revision Fri Dec 7, 2007 In the early years of the twentieth century, Gottlob Frege and David Hilbert, two titans of mathematical logic, engaged in a controversy regarding the correct understanding of the role of axioms in mathematical theories, and the correct way to demonstrate consistency and independence results for such axioms. The controversy touches on a number of difficult questions in logic and the philosophy of logic, and marks an important turning-point in the development of modern logic. This entry gives an overview of that controversy and of its philosophical underpinnings. 1. Introduction 2. Hilbert's Foundations of Geometry 4. The Deeper Disagreement ... Related Entries 1. Introduction Grundlagen der Geometrie Nineteenth Century Geometry ; for the role of Hilbert's work in the development of model theory, see model theory The correspondence and essays involved in the Frege-Hilbert debate shed light both on the emergence, at the turn of the 20

33. Brunner: A Modal Logic Of Consistency A modal logic of Consistency. Rendiconti del Seminario Matematico della of the FraenkelMostowski method for proving independence results about the http://www.numdam.org/numdam-bin/fitem?id=RSMUP_1995__93__143_0

34. Springer Online Reference Works Another form of this manner of proving the independence of is to establish the . Among the results obtained concerning the Consistency of formal systems, http://eom.springer.de/a/a014300.htm

Encyclopaedia of Mathematics A Article referred from Article refers to Axiomatic method A way of arriving at a scientific theory in which certain primitive assumptions, the so-called axioms (cf. Axiom ), are postulated as the basis of the theory, while the remaining propositions of the theory are obtained as logical consequences of these axioms. 19th century Elements (ca. 300 B.C. The discovery of a non-Euclidean geometry by N.I. Lobachevskii and J. Bolyai at the beginning of the 19th century Euclid concerning parallel lines is replaced by its negation, then it is possible to develop in a purely logical manner a geometry which is just as elegant and meaningful as is Euclidean geometry. The attention of mathematicians of the 19th century M. Pasch G. Peano and D. Hilbert proof theory as one of the main chapters of modern mathematical logic. It was recognized as early as the 19th century that foundations must be created for mathematics and for the relevant mathematical problems. It was mainly in analysis that the basic concepts were rendered more precise, and that more complex ideas were reduced to simpler concepts by methods involving increasingly rigorous logical reasoning (the language of A.L. Cauchy

35. To The IL Services Unit has credited ILC’s with systems change results for We will periodically review our internal practices to ensure Consistency and http://www.vesid.nysed.gov/lsn/ilc/1103memo.html

To: All Independent Living Centers Date: November 26, 2003 From: Robert Gumson Subject: Field memo regarding improving consistency in community and systems change results reporting This memorandum seeks to clarify parameters and remedy inconsistencies in the Office of Vocational and Educational Services for Individuals with Disabilities (VESID), Independent Living Service Unit’s review and approval of achievement of Independent Living Center goals and outcomes of community and systems change initiatives. Any changes to the review parameters listed below are effective immediately and are to be reflected accordingly in 2003-2004 mid year report and end of year report. The content of the memorandum derives from input from six Independent Living Centers including: ARISE Inc., Center for the Independence of the Disabled in New York, Independent Living Project of Western New York, North Country Center for Independence, and the Independent Living Center of the Hudson Valley. Representatives from these centers met with VESID in October, following a discussion of this topic at the New York State Independent Living Council’s Fall 2003 statewide conference workshop presented by Fred Ayers and myself, entitled “The Art of Systems Change Goal Planning.” The issues addressed and positions arrived at to improve systems advocacy goal reporting as a result of the meeting are as follows: Definition: The group held an engaging dialogue on the current definition of “systems change” adopted within New York State’s CIL Standards, Performance Measures and Data Collection Guide, October 2002 as follows:

36. Papers In Elementary Proof Theory 1998--2002. \\ A Reasoned Bibliography\\ Sara As byproducts, bounds for proof search for various classes of formulas are obtained, as well as syntactic proofs of Consistency and independence. http://www.helsinki.fi/~negri/ptpub.html

Papers in elementary proof theory 1998-2002. A reasoned bibliography Sara Negri and Jan von Plato N.B.: Links to files are being added. Elementary proof theory has its origins in Hilbert's program that in its beginnings tried to study the structure of mathematical proofs by finitary means. This led to success in pure logic, in Gentzen's systems of natural deduction and sequent calculi, but failed whenever arithmetic with full induction was part of a system. The first results of our work in elementary proof theory appeared in 1998. One could think that seventy years after Gentzen, there can not be much to say about the proof theory of propositional and predicate logic. Instead, even the relation between Gentzen's two main formulations, natural deduction and sequent calculus, has not been completely cleared before. Within sequent calculus, it has been possible to give new formulations of the logical rules with interesting properties, such as our ``sequent calculus in natural deduction style,'' as well as new proofs of old results. A prime example of the latter is the proof of Gentzen's cut elimination theorem without the ``mix rule,'' Gentzen's method for hiding the problematic case of cut preceded by contraction. A reviewer said of our proof that ``it is surprising that it has taken over half a century since Gentzen's original work to reach this result.'' (M. Takano, Math. Reviews

37. Perspectives In Logic - List Of Books In addition to particular Consistency results, the author shows methods which can be used for such independence results. Many of the results are presented http://www.aslonline.org/books-perspectives-list.html

Books Lecture Notes in Logic Perspectives in Logic Other ASL Books ... Member Discounts Perspectives in Mathematical Logic This book series is now being published by the Association for Symbolic Logic on its own; the previous collaboration with Springer-Verlag came to an end on April 30, 2001. Thanks to the generosity of Springer-Verlag, ASL will distribute the available stock of certain books in the series to the logic community at a low price (as has been done with the existing stock of books in the Lecture Notes in Logic ). Some books in the series will continue to be made available by Springer-Verlag and others will be reprinted by ASL. At the moment (October 2001) the situation is in flux and plans for the future are being made. Inquiries may be made via the ASL business office : Association for Symbolic Logic Box 742, Vassar College 124 Raymond Avenue Poughkeepsie, New York 12604 USA Email: asl@vassar.edu

38. The Future Of Set Theory By S.Shelah i.e. is a proof of Consistency from the Consistency of ``ZFC+ super compact a . This is in general a good justification for independence results; http://shelah.logic.at/E16/E16.html

Abstract: Judah has asked me to speak on the future of set theory, so as the next millennium is coming, to speak on set theory in the next millennium. But we soon cut this down to set theory in the next century. Later on I thought I had better cut it down to dealing with the next decade, but I suspect I will speak on what I hope to try to prove next year, or worse - what I have done in the last year (or twenty). It seems I am not particularly suitable for such a lecture, as I have repeatedly preferred to try to prove another theorem than to prepare the lecture (or article); so why did I agree at all to such a doubtful endeavor? Well, under the hypothesis that I had some moral obligation to help Haim in the conference (and the proceedings) and you should not let a friend down, had I been given the choice to help with organizing the dormitories, writing a lengthy well written expository paper or risking making fool of myself in such a lecture, I definitely prefer the latter. The Future of Set Theory Saharon Shelah Institute of Mathematics The Hebrew University of Jerusalem 91904 Jerusalem, Israel

39. IngentaConnect New Moduli Spaces From String Background Independence Consistency New moduli spaces from string background independence Consistency conditions Our results also imply a partial antibracket cohomology theorem for the http://www.ingentaconnect.com/content/els/05503213/1996/00000480/00000003/art005

var tcdacmd="dt"; Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); New moduli spaces from string background independence consistency conditions Author: Zwiebach B. Source: Nuclear Physics B , Volume 480, Number 3, 2 December 1996 , pp. 507-540(34) Publisher: Elsevier view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Language: English Document Type: Research article DOI: Affiliations: Center for Theoretical Physics, Laboratory of Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

40. Logic Seminar Abstracts Winter 2003 Arithmetic independence results using higher recursion theory application of this kind of independence proof, concerning Consistency sentences for PA. http://www-logic.stanford.edu/Abstracts/Seminar/Winter04.html

Logic Seminar Abstracts Winter 2003 Boris Konev (Steklov Institute of Mathematics at St.Petersburg and The University of Liverpool) Monodic Temporal Resolution Until recently, First-Order Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et.al., identifying a finitely axiomatisable fragment, termed the monodic fragment, has led to improved understanding of FOTL. Yet, in order to utilise these theoretical advances, it is important to have appropriate proof techniques for this monodic fragment. In this talk, we modify and extend the clausal temporal resolution technique, originally developed for propositional temporal logics, to enable its use in such monodic fragments. We develop a specific normal form for monodic formulae in FOTL, and provide a complete resolution calculus for formulae in this form. Not only is this clausal resolution technique useful as a practical proof technique for certain monodic classes, but the use of this approach provides us with increased understanding of the monodic fragment. In particular, we here show how several features of monodic FOTL can be established as corollaries of the completeness result for the clausal temporal resolution method. These include definitions of new decidable monodic classes, simplification of existing monodic classes by reductions, and completeness of clausal temporal resolution in the case of monodic logics with expanding domains, a case with much significance in both theory and practice.

41. JNNP -- Sign In Page Table 1 Distribution, internal Consistency, validity, and responsiveness of the motor subscale of the functional independence measure (FIM), http://jnnp.bmj.com/cgi/content/full/73/2/188

HOME HELP FEEDBACK SUBSCRIPTIONS ... REGISTER Author Keyword(s) Vol Page [Advanced] This article is FREE for registered users. Please log in or complete a one-time Registration process. Full Text Comparison of the psychometric characteristics of the functional independence measure,... Hsueh et al. J Neurol Neurosurg Psychiatry. To view this item, select one of the options below: Login via Athens Login for subscribers/registrants User Name Sign in without cookies. Can't get past this page? Help with Cookies. Need to Activate? Password Forgotten your user name or password? Subscribe Buy the article SitePass - You may access all content in Journal of Neurology, Neurosurgery, and Psychiatry Online (from the computer you are currently using) for 30 days. Regain access to an already purchased article if the access period has not yet expired. Register for Access - all archive content published more than 12 months ago requires a FREE registration. This Article Abstract Full Text (PDF) Submit a response ... Alert me if a correction is posted Services Email this link to a friend Similar articles in this journal Similar articles in PubMed Add article to my folders ... Request Permissions Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Hsueh, I-P

42. The Journal Of Nervous And Mental Disease - UserLogin Previous research has generally confirmed internal Consistency, testretest reliability, and scale independence of the ASI (Kosten et al., 1983; http://www.jonmd.com/pt/re/jnmd/fulltext.00005053-199703000-00005.htm;jsessionid

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43. Colloquium Logicum 2004, Abstracts We show the Consistency of the various rigidity levels (assuming Jensen s . Gina Kolata reported about celebrated independence results for first order http://www.math.uni-heidelberg.de/logic/CL_2004/abstracts.html

COLLOQUIUM LOGICUM 2004 Biannual Meeting of the German Society for Mathematical Logic (DVMLG) September 17 - 19, 2004 Heidelberg (Germany) LIST OF TALKS WITH ABSTRACTS Invited Lectures: Albert Atserias (Barcelona): The complexity of random 3-SAT: a survey and new results S. Barry Cooper (Leeds): Incomputability, fifty years after Alan Turing Ulrich Kohlenbach (Darmstadt): Applications of logic to nonlinear functional analysis Javier Legris (Buenos Aires): The many faces of logicism. On the interrelations between symbolic logic and foundations of mathematics at the end of the 19th century Janos A. Makowsky 50 years of the Spectrum Problem: History and new directions Amador Martin-Pizarro Supersimple fields Ralf Schindler Cardinal arithmetic and determinacy Peter Schuster On constructing completions (Talk at DMV-conference) Andreas Weiermann (Utrecht): Classifying the phase transition for independence results PhD-Colloquium: Joost Joosten (Utrecht): Worms, interpretations and proof strength Jan Reimann (Heidelberg): Hausdorff dimension, randomness, and entropy

44. Philosophy Papers Online: Browse Papers Two manners of expressing a system s Consistency are presented the Godel Consistency Arithmetical independence results using higher recursion theory http://phonline.org/papers.php?area=PhilMath

45. Primary Sources Its results were astounding in their day, nearly half a century ago. .. If Consistency of independence or conformity in behavior is shown to be a fact, http://www.wadsworth.com/psychology_d/templates/student_resources/0155060678_rat

Primary Sources Social psychology studies the nature and causes of behavior and mental processes in social situations. Social psychologists have noted that people and lower animals often behave differently when they are by themselves or in the presence of others. When people alter the thoughts, feelings, and behavior of other people, they are said to exert social influence. Two of the key topics in the psychology of social influence are obedience and conformity. We are said to conform when we change our behavior in order to adhere to social norms. For example, we tend to conform to social norms by facing front in elevators and whispering in libraries. Conformity is often a good thing because many social norms promote comfort and survival. But conformity to social norms can also promote maladaptive or dangerous behavior, as when teenagers engage in risky behavior because of the belief that "everyone’s doing it." Opinions and Social Pressure By SOLOMON E. ASCH

46. Media Centre: Speeches - Consistency In Decision Making Tension clearly exists between the need for Consistency and the independence of decision makers. Some would argue that the two are incompatible. http://www.irb-cisr.gc.ca/en/media/speeches/2000/ccat_e.htm

Contact Us Help Search Canada Site ... Decisions CONSISTENCY IN DECISION MAKING Council of Canadian Administrative Tribunals Ottawa, Ontario June 12, 2000 by Peter Showler Chairperson Immigration and Refugee Board (Check against delivery) I am pleased to be here today and I want to thank the Council of Canadian Administrative Tribunals for inviting me to speak to you about issues of "consistency in decision making" as this concept relates to independence and accountability. After having accepted the position of Chairperson, my perspective on these same issues has altered considerably. I confess to having a more managerial view of individual decision makers and to being more conscious of the IRB as an independent institution that is accountable to the courts, to the public and to the government. Black's Law Dictionary defines "independence" as a state or condition of being free from dependence, subjection or control and "accountability" as a state of being responsible or answerable. Finally, "consistency" is defined in the Oxford Dictionary as "the quality, state, or fact of being consistent; agreement, harmony, compatibility". Each term has its own legal meaning but I am interested in the interaction between the three. On its face, it would appear that consistency in decision making is incompatible with independence and that independence is incompatible with accountability. I would suggest that these three concepts are not incompatible with each other but rather that a balance must be struck between them such that the administration of justice in a tribunal is realized.

47. Tennenbaum S Theorem Nor have any of the classical numbertheoretical problems yielded to logical methods of proving independence. Only the last problem, independence results http://web.mat.bham.ac.uk/R.W.Kaye/papers/tennenbaum/tennhistory

Tennenbaum's Theorem Some historical background The theorem known as Tennenbaum's Theorem was given by Stanley Tennenbaum in a paper at the April meeting in Monterey, California, 1959, and published as a one-page abstract in the Notices of the American Mathematical Society . It is easily stated as saying that there is no nonstandard recursive model of Peano Arithmetic, and is an attractive and rightly often-quoted result. This paper celebrates Tennenbaum's Theorem; we state the result fully and give a proof of it and other related results later. This introduction is in the main historical. The goals of the latter parts of this paper are: to set out the connections between Tennenbaum's Theorem for models of arithmetic and the G¶del–Rosser Theorem and recursively inseparable sets; and to investigate stronger versions of Tennenbaum's Theorem and their relationship to some diophantine problems in systems of arithmetic. Tennenbaum's theorem was discovered in a period of foundational studies, associated particularly with Mostowski, where it still seemed conceivable that useful independence results for arithmetic could be achieved by a hands-on approach to building nonstandard models of arithmetic. Mostowski's own aspirations for the programme are clearly set out in his address to the 8th Congress of Polish mathematicians in September 1953

48. Sequence-matched Probes Produce Increased Cross-platform Consistency And More Re We report here that restricting analysis to sequencematched probes produces a higher level of Consistency between results derived from alternative http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=419626