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 1. JSTOR Effectively Retractable Theories And Degrees Of Undecidability We identify a sentence with its Godel number so that we speak of 0 sets of . degrees OF Undecidability 601 resulting sequence of sentences, say do, d~,.http://links.jstor.org/sici?sici=0022-4812(196912)34:4<597:ERTADO>2.0.CO;2-3

2. 03Dxx
Other Turing degree structures; 03D30 Other degrees and reducibilities; 03D35 Undecidability and degrees of sets of sentences; 03D40 Word problems, etc.
http://www.ams.org/msc/03Dxx.html

3. List For KWIC List Of MSC2000 Phrases
sentences decidability of theories and sets of 03B25 sentences Undecidability and degrees of sets of 03D35 separability 54D65
http://www.math.unipd.it/~biblio/kwic/msc/m-kl_11_48.htm
 semigroupoids, semigroups, groups (viewed as categories) # groupoids, semigroups semigroups # $C$- semigroups # analysis on topological semigroups # commutative semigroups # integrated semigroups # inverse semigroups # mappings of semigroups # orthodox semigroups # regular semigroups # representations of general topological groups and semigroups # structure of topological semigroups # transformation groups and semigroups # varieties of semigroups and applications to diffusion processes # Markov semigroups and linear evolution equations # one-parameter semigroups and monoids # ordered semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions # almost periodic functions on groups and semigroups in $C^*$-algebras # derivations, dissipations and positive semigroups in automata theory, linguistics, etc. semigroups of linear operators # groups and semigroups of linear operators, their generalizations and applications # groups and semigroups of nonlinear operators semigroups of nonlinear operators # groups and semigroups of rings # semigroup rings, multiplicative

4. Mhb03.htm
03D28, Other Turing degree structures. 03D30, Other degrees and reducibilities. 03D35, Undecidability and degrees of sets of sentences
http://www.mi.imati.cnr.it/~alberto/mhb03.htm

5. Sachgebiete Der AMS-Klassifikation: 00-09
deductive systems 03B25 Decidability of theories and sets of sentences, reducibilities 03D35 Undecidability and degrees of sets of sentences 03D40
http://www.math.fu-berlin.de/litrech/Class/ams-00-09.html
##### nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen
01-XX 03-XX 04-XX 05-XX 06-XX 08-XX
##### nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen

 6. MathNet-Mathematical Subject Classification 03D25, Recursively enumerable sets and degrees. 03D30, Other degrees; reducibilities. 03D35, Undecidability and degrees of sets of sentenceshttp://basilo.kaist.ac.kr/API/?MIval=research_msc_1991_out&class=03-XX

 7. HeiDOK 03D35 Undecidability and degrees of sets of sentences ( 0 Dok. ) 03D40 Word problems, etc. ( 0 Dok. ) 03D45 Theory of numerations, effectively presentedhttp://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03D&anzahl

8. DC MetaData For:The Halting Problem For Additive Machines Is Not Decidable By An
68Q10 Modes of computation 03D25 Recursively enumerable sets and degrees 03D35 Undecidability and degrees of sets of sentences 68Q65 Abstract data types;
##### The Halting Problem for Additive Machines is Not Decidable by an Additive Machine with the Rational Numbers as an Oracle
Preprint series: Preprintreihe Mathematik 2006, 4 MSC 2000
68Q10 Modes of computation 03D25 Recursively enumerable sets and degrees 03D35 Undecidability and degrees of sets of sentences 68Q65 Abstract data types; algebraic specification 68Q17 Computational difficulty of problems
Abstract
We answer the question posed by Klaus Meer and Martin Ziegler in "Uncomputability below the Real Halting Problem" whether the set of rational numbers is strictly easier than the Halting Problem with respect to additive machines. We define a problem below the Halting Problem such that the set of rational numbers is strictly easier than the new problem. As a consequence, the set of rational numbers is strictly easier than the Halting Problem. This document is well-formed XML.

9. DC MetaData For: Decidability Of Code Properties
See also {20M35, 03D35 Undecidability and degrees of sets of sentences We explore the borderline between decidability and Undecidability of
 Decidability of Code Properties by H. Fernau, K. Reinhardt, L. Staiger Preprint series: 00-11, Reports on Computer Science The paper is published: in: Proc. Developments in Language Theory IV (G.Â Rozenberg and W.Â Thomas Eds.), World Scientific, Singapore 2000, 153 - 163. MSC 03D35 Undecidability and degrees of sets of sentences CR Abstract We explore the borderline between decidability and undecidability of the following question: Keywords: partially blind counter machines, prefix code, infix code, bifix code, deciphering delay, decidability Upload: Update: The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.

10. DC MetaData For: Decidability Of Chaos For Some Families Of Dynamical Systems
MSC 2000 37C99 None of the above, but in this section 03D35 Undecidability and degrees of sets of sentences. Preprint Server.
Decidability of chaos for some families of dynamical systems Source file as Postscript Document (.ps) Portable Document Format (.pdf) Alexander Arbieto Carlos Matheus Keywords:
Decidability, chaos, lyapunov exponents, SRB measues, topological entropy. Abstract:
MSC 2000:

37C99 None of the above, but in this section
03D35 Undecidability and degrees of sets of sentences Preprint Server

we shall consider not only sentences but also formulas with free .. On the structure of degrees of index sets. Algebra and Logic (1979) 18463Â480.
http://logcom.oxfordjournals.org/cgi/content/full/exm038v1

 12. General General Mathematics Mathematics For Nonmathematicians systems Decidability of theories and sets of sentences See also 11U05, 12L05, Undecidability and degrees of sets of sentences Word problems, etc.http://amf.openlib.org/2001/msc2000.xsd

 13. 359/369 (Total 5522) NO 152 03E04 Ordered Sets And Translate this page See also 06B25, 08A50, 20F10, 68R15. 139, 03D35, Undecidability and degrees of sets of sentences. 138, 03D30, Other degrees and reducibilitieshttp://www.mathnet.or.kr/mathnet/msc_list.php?mode=list&ftype=&fstr=&page=359

 14. CatÃ¡logo Translate this page BÃºsqueda por tema 03D35 - Undecidability and degrees of sets of sentences Martin Weese, Undecidable extensions of the theory of Boolean algebrashttp://catalis.uns.edu.ar/cgi-bin/catalis_pack_demo_devel/wxis?IsisScript=opac/x

 15. 0 Top The TOP Concept In The Hierarchy. 1 Adverbial Modification 308 degrees of sets of sentences 309 effectively presented structure 31 329 thue system 33 unicorn 330 Undecidability 331 word problem 332 reference Thehttp://staff.science.uva.nl/~caterina/LoLaLi/soft/ch-data/gloss.txt

16. Richard A. Shore: Publications
On the AEsentences of alpha-recursion theory, in Generalized Recursion Theory II, . The theories of the T, tt and wtt r.e. degrees Undecidability and
http://www.math.cornell.edu/~shore/publications.html
##### Richard A. Shore : Publications
Curriculum Vitae Most of the documents below with electronic versions have been compiled for optimum viewing in PDF format. However, some papers (for various reasons) look grainy as PDF files. All the papers with electronic versions are, however, also available in postscript and DVI format.
• On large cardinals and partition relations, Journal of Symbolic Logic (1971), 305-308 (with E.M. Kleinberg).
• Weak compactness and square bracket partition relations, Journal of Symbolic Logic (1972), 673-676 (with E.M. Kleinberg).
• Square bracket partition relations in L Fundamenta Mathematica
• Minimal alpha-degrees, Annals of Mathematical Logic
• Cohesive sets: countable and uncountable, Proceedings of the American Mathematical Society
• Sigma n sets which are Delta n -incomparable (uniformly), Journal of Symbolic Logic
• Splitting an alpha-recursively enumerable set, Transactions of the American Mathematical Society
• The recursively enumerable alpha-degrees are dense, Annals of Mathematical Logic
• The irregular and non-hyperregular alpha-r.e. degrees
• 17. Publication Of V.L. Selivanov
On the structure of degrees of index sets. Algebra and Logic, 18, . Undecidability in the homomorphic quasiorder of finite labeled forests (joint with
http://vseliv.nspu.ru/en/publ/part
Title page Curriculum vitae Publication Research Photoalbum
##### Papers refereed by journal standards
1. On computability of some classes of numberings. Prob. Methods and Cybernetics, v.12-13, Kazan University, Kazan,1976, 157170 (Russian). 2. On numberings of families of total recursive functions. Algebra and Logic, 15, N 2 (1976), 205226 (Russian, there is an English translation). 3. Two theorems on computable numberings. Algebra and Logic, 15, N 4 (1976), 484 (Russian, there is an English translation). 4. Numberings of canonically computable families of finite sets. Sib. Math. J., 18, N 6 (1977), 13731381 (Russian, there is an English translation). 5. On index sets of classes of numberings. Prob. Methods and Cybernetics, v.14, Kazan University, Kazan,1978, 90103 (Russian). 6. On index sets of computable classes of finite sets. In: Algorithms and Automata, Kazan University, Kazan,1978, 9599 (Russian). 7. Some remarks on classes of recursively enumerable sets. Sib. Math. J., 19, N 1 (1978), 109115. 8. On the structure of degrees of index sets. Algebra and Logic, 18, N 4 (1979), 286299.

 18. CARNEGIE MELLON UNIVERSITY PROGRAM IN PURE AND APPLIED LOGIC LOGIC Robert Soare, /Recursively Enumerable sets and degrees/, Springer. The famous incompleteness, Undecidability and undefinability results of Godel andhttp://logic.cmu.edu/pal-courses-s05.txt

19. Tree Structure Of LoLaLi Concept Hierarchy Updated On 2004624
330 Undecidability . . . . 328 theory of numerations . 308 degrees of sets of sentences . . . . 319 recursive equivalence type .
http://remote.science.uva.nl/~caterina/LoLaLi/soft/ch-data/tree.txt

20. Hilary Putnam Bibliography
ÂDecidability and Essential Undecidability.Â Journal of Symbolic Logic 22.1 (March 1957) . Âdegrees of Unsolvability of Constructible sets of Integers.
http://www.pragmatism.org/putnam/
 A Bibliography of Publications by Hilary Putnam Books [For tables of contents of these books, see below in the chronological listing of all publications] The Meaning of the Concept of Probability in Application to Finite Sequences . Ph.D. dissertation, University of California, Los Angeles, 1951. New York: Garland, 1990. Philosophy of Mathematics: Selected Readings . Edited with Paul Benacerraf. Englewood Cliffs, N.J.: Prentice-Hall, 1964. 2nd ed., Cambridge: Cambridge University Press, 1983. Philosophy of Logic . New York: Harper and Row, 1971. London: George Allen and Unwin, 1972. Mathematics, Matter and Method Philosophical Papers , vol. 1. Cambridge: Cambridge University Press, 1975. 2nd. ed., 1985. Mind, Language and Reality Philosophical Papers , vol. 2. Cambridge: Cambridge University Press, 1975. Meaning and the Moral Sciences . London: Routledge and Kegan Paul, 1978. Reason, Truth, and History . Cambridge: Cambridge University Press, 1981. Realism and Reason Philosophical Papers , vol. 3. Cambridge: Cambridge University Press, 1983. Methodology, Epistemology, and Philosophy of Science: Essays in Honour of Wolfgang StegmÃ¼ller

21. Springer Online Reference Works
Both natural and programming languages can be viewed as sets of sentences, that is, finite strings of elements from some basic vocabulary.
http://eom.springer.de/F/f040850.htm
 Encyclopaedia of Mathematics F Article referred from Article refers to Formal languages and automata Both natural and programming languages can be viewed as sets of sentences, that is, finite strings of elements from some basic vocabulary. The notion of a language introduced below is very general. It certainly includes both natural and programming languages and also all kinds of nonsense languages one might think of. Traditionally, formal language theory is concerned with the syntactic specification of a language rather than with any semantic issues. A syntactic specification of a language with finitely many sentences can be given, at least in principle, by listing the sentences. This is not possible for languages with infinitely many sentences. The main task of formal language theory is the study of finitary specifications of infinite languages. The basic theory of computation, as well as of its various branches, such cryptography Turing machine Automaton, finite Grammar, formal ... Automata, theory of An alphabet is a finite non-empty set. The elements of an alphabet

22. Computability Theory
Post asked whether there is an intermediate c.e. degree and this was solved by Friedberg and .. We define Rosser sentences and show their Undecidability.
http://caltechmacs117b.wordpress.com/
##### Goodstein sequences
July 27, 2007 by andrescaicedo Will Sladek, a student at Caltech, wrote an excellent introductory paper on incompleteness in PA, The termite and theÃÂ tower . While Will was working on his paper, I wrote a short note, GoodsteinÃ¢ÂÂsÃÂ function Posted in Undecidability and incompleteness
##### Unsolvable problems - Lecture 3
March 12, 2007 by andrescaicedo At the beginning of the course we built (recursively in ) two incomparableÃÂ sets A,B . It follows that A and B ÃÂ have degrees intermediate between and . The construction required that we fixed finite initial segments of A and B ÃÂ during an inductive construction and so it is not clear whether they are c.e. or not. (A c.e. construction would add elements toÃÂ a set and we would not have complete control on what is kept out of the set). Post asked whether there is an intermediate c.e. degree and this was solved by Friedberg and Muchnik using what is now called a finite injury priority construction. We show this construction; again, 2 incomparable sets A and B are built and the construction explicitly shows they are c.e. This implies they are not recursive and have degree strictly below

23. 1. Computability And Randomness Higher Randomness Notions And
The theory of the polynomial manyone degrees of recursive sets is undecidable (with K.Ambos-Spies). STACS 92, Lecture Notes in Computer Science 577,
http://www.cs.auckland.ac.nz/~nies/onlinepapers.html
 1. Computability and Randomness Higher randomness notions and their lowness properties (with Chitat Chong and Liang Yu). Israel J. Math, To appear Eliminating concepts. To appear in Proc. of the IMS workshop on computational aspects of infinity, Singapore. Lowness for Computable Machines (with Rod Downey, Noam Greenberg and Nenad Mikhailovich). To appear in Proc. of the IMS workshop on computational aspects of infinity, Singapore. A lower cone in the wtt degrees of non-integral effective dimension (with Jan Reimann). To appear in Proc. of the IMS workshop on computational aspects of infinity, Singapore. Non-cupping and randomness. Proc. Amer. Math. Soc. 135 (2007), no. 3, 837844. (with Rod Downey, Rebecca Weber, and Liang Yu). Journal of Symbolic logic 71( 3), 2006, pp. 1044-1052. Randomness via effective descriptive set theory (with Greg Hjorth). J. London Math Soc Nies 75 (2): 495-508. Calibrating randomness. Bull. Symb. Logic. 12 no 3 (2006) 411-491 (with Downey, Hirschfeldt and Terwijn). Randomness and computability: Open questions (with Joe Miller). Bull. Symb. Logic. 12 no 3 (2006) 390-410.

24. Mathematical Preprints By Steffen Lempp
The Pi3theory of the enumerable Turing degrees is undecidable, with andrÃ© Nies .. in terms of congruences and effective conjunctions of Pi01-sentences.
http://www.math.wisc.edu/~lempp/papers/list.html
##### Mathematical Preprints by Steffen Lempp
(The preprints are listed by research area, within research area in alphabetical order of coauthor(s).)
##### Research Areas
• Classical Computability Theory
##### Lattice embeddings into the c. e. degrees
• Lattice embeddings into the r. e. degrees preserving and 1 , with Klaus Ambos-Spies and Manuel Lerman (published in Journal of the London Mathematical Society, 1994, ps download of paper
Abstract: We show that a finite distributive lattice can be embedded into the r. e. degrees preserving least and greatest element iff the lattice contains a join-irreducible noncappable element.
• Lattice embeddings into the r. e. degrees preserving 1 , with Klaus Ambos-Spies and Manuel Lerman (published in "Logic and Philosophy of Science: Papers from the 9th International Congress of Logic, Methodology, and Philosophy of Science", 1994, ps download of paper , jpg download of Diagram 1 in preparation)
Abstract: We show that the two nondistributive five-element lattices, M

25. North Texas Logic Conference
Logic, 1997 proved the Undecidability of the firstorder theory of the enumeration degrees of the 02-sets. A closer analysis of their proof shows that
http://www.math.unt.edu/logic/ntlc/ntlc.html
##### OctoberÂ 8 th th
UNT Logic Schedule Abstracts Future Directions ... Transportation
##### Schedule
All talks will be held in GAB 105. The official program can be found here Friday, October 8 Saturday, October 9 Sunday, October 10 Morning Session: Morning Session: Morning Session: Andreas Blass Julia Knight
Steffen Lempp

Ilijas Farah
...
Benedikt Loewe
Break For Lunch Break For Lunch Break For Lunch Afternoon Session: Afternoon Session: Afternoon Session: Dan Mauldin
Reed Solomon

Millican Lecture
Ted Slaman

Denis Hirschfeldt

Peter Cholak
Peter Komjath ...
Future Directions
Contributed Talks
Thomas Kent
Alexander Raichev Bart Kastermans Ross Bryant ... Charles Boykin Dinner Trail Dust
##### Abstracts
Becker Title: Cocycles Abstract: This talk is a contribution to the descriptive set theory of Polish group actions. Like much of the recent research in this field, it is concerned with a known theorem about locally compact groups and with the question of whether or to what extent the result generalizes to arbitrary Polish groups. The theorem in question is Mackey's Cocycle Theorem: Every almost cocycle is equivalent to a strict cocycle. This question is relevant to the foundations of quantum mechanics. Blass Title: Abstract State Machines and Choiceless Polynomial Time Abstract: Choiceless polynomial time is a complexity class of decision problems whose instances are finite structures. The polynomial-time computations here are not permitted to use an ordering of the input structure (or, what amounts to the same thing, arbitrary choices), but parallelism and rich data structures are allowed. The underlying computational framework is given by Gurevich's abstract state machines, to which I'll provide a brief introduction. Then I'll discuss what can (and what cannot) be computed in choiceless polynomial time, particularly when it is augmented by an oracle for cardinality. My work in this area is joint with Yuri Gurevich and Saharon Shelah.

 26. Studia Informatica AbstractThe degree of Undecidability of nonmonotonic logic is investigated. arithmetical but not recursively enumerable sets of sentences definable byhttp://www.studiainformatica.ii.ap.siedlce.pl/volume.php?id=7

27. Olivier Finkel
The stretching theorem for local sentences expresses a remarkable reflection . Undecidability of Topological and Arithmetical Properties of Infinitary
http://www.logique.jussieu.fr/www.finkel
##### Olivier Finkel
Ãquipe ModÃ¨les de Calcul et ComplexitÃ©
et Institut des SystÃ¨mes Complexes
CNRS et ENS LYON
69364 Lyon Cedex 07
FRANCE E-Mail: Olivier.Finkel_at_ens-lyon.fr
##### ThÃ¨mes de Recherche
ThÃ©orie des ModÃ¨les des Formules Locales

Omega Langages Rationnels, AlgÃ©briques, Localement Finis
##### Research Areas
Model Theory of Local Sentences Descriptive Complexity Finite Model Theory Regular, Context Free, and Locally Finite Omega Languages Infinitary Rational Relations Topological Properties of Omega Languages Finite Machines Winning Strategies in Infinite Games Timed Automata and Timed Languages Cellular Automata
##### Publications
• Journal papers Conference papers Thesis Habilitation ... Some talks
• ##### Langages de BÃ¼chi et Omega Langages Locaux

28. Boolos Bibliography
(with Hilary Putnam) degrees of unsolvability of constructible sets of Extremely undecidable sentences. Journal of Symbolic Logic 47 (1982) 191196.
http://web.mit.edu/philos/www/facultybibs/boolos_bib.html
 George Boolos: List of Publications 1. (with Hilary Putnam) "Degrees of unsolvability of constructible sets of integers." Journal of Symbolic Logic 2. "Effectiveness and natural languages." In S. Hook, ed., Language and Philosophy . New York University Press, 1969. 3. "On the semantics of the constructible levels." Zeitschrift fÃ¼r mathematische Logik und Grundlagen der Mathematik 4. "A proof of the LÃ¶wenheim-Skolem theorem." Notre Dame Journal of Formal Logic 5. "The iterative conception of set." Journal of Philosophy 68 (1971) 215-231. Reprinted in Logic, Logic, and Logic and in Benacerraf, P. and Putnam, H., eds. Philosophy of Mathematics: Selected Readings , second ed. Cambridge: Cambridge University Press, 1984, pp. 486-502. 6. "A note on Beth's theorem." Bulletin de l'Academie Polonaise des Sciences 7. "Arithmetical functions and minimization." Zeitschrift fÃ¼r mathematische Logik und Grundlagen der Mathematik 8. "Reply to Charles Parsons' 'Sets and classes' (1974)" First published in Logic, Logic, and Logic

29. Sentence Modeling And Parsing
Parsing is the process of discovering analyses of sentences, that is, consistent sets of relationships between constituents that are judged to hold in a
http://cslu.cse.ogi.edu/HLTsurvey/ch3node8.html
Next: 3.7 Robust Parsing Up: 3 Language Analysis and Previous: 3.5 Semantics
##### 3.6 Sentence Modeling and Parsing
Fernando Pereira
The complex hidden structure of natural-language sentences is manifested in two different ways: predictively , in that not every constituent (for example, word) is equally likely in every context, and evidentially , in that the information carried by a sentence depends on the relationships among the constituents of the sentence. Depending on the application, one or the other of those two facets may play a dominant role. For instance, in language modeling for large-vocabulary connected speech recognition , it is crucial to distinguish the relative likelihoods of possible continuations of a sentence prefix , since the acoustic component of the recognizer may be unable to distinguish reliably between those possibilities just from acoustic evidence . On the other hand, in applications such as machine translation or text summarization , relationships between sentence constituents, such as that a certain noun phrase is the direct object of a certain verb occurrence, are crucial evidence in determining the correct translation or summary. Parsing is the process of discovering analyses of sentences, that is, consistent sets of relationships between constituents that are judged to hold in a given sentence, and, concurrently, what the constituents are, since constituents are typically defined inductively in terms of the relationships that hold between their parts.

30. Computability Complexity Logic Book
Reduction concepts and degrees of unsolvability. 114 Reduction concepts (theorem of Post), index sets (theorem of Rice and Shapiro, Sncomplete program
http://www.di.unipi.it/~boerger/cclbookcontents.html
 Studies in Logic and the Foundations of Mathematics, vol. 128, North-Holland, Amsterdam 1989, pp. XX+592. CONTENTS Graph of dependencies XIV Introduction XV Terminology and prerequisites XVIII Book One ELEMENTARY THEORY OF COMPUTATION 1 Chapter A. THE MATHEMATICAL CONCEPT OF ALGORITHM 2 PART I. CHURCH'S THESIS 2 1. Explication of Concepts. Transition systems, 2 Computation systems, Machines (Syntax and Semantics of Programs), Turing machines. structured (Turing- and register-machine) programs (TO, RO). 2. Equivalence theorem, 26 LOOP-Program Synthesis for primitive recursive functions. 3. Excursus into the semantics of programs. 34 Equivalence of operational and denotational semantics for RM-while programs, fixed-point meaning of programs, proof of the fixed-point theorem. 4*. Extended equivalence theorem. Simulation of 37 other explication concepts: modular machines, 2-register machines, Thue systems, Markov algorithms, ordered vector addition systems (Petri nets), Post calculi (canonical and regular), Wang's non-erasing half-tape machines, word register machines. 5. Church's Thesis 48

31. Annals Of Pure And Applied Logic
Decidable and undecidable prime theories in infinitevalued logic On Sigma1 and Pi1 sentences and degrees of Interpretability. by Per LindstrÃ¶m v.
http://wotan.liu.edu/docis/dbl/apuapl/index.html
 The Digital Librarian's Digital Library search D O CISÃÂ  Do cumentsÃÂ inÃÂ  C omputing and I nformationÃÂ  S cience Home Journals and Conference Proceedings Annals of Pure and Applied Logic On gaps under GCH type assumptions by:ÃÂ  Moti Gitik v. 119 i. 1-3 p. 1 - 18 Thue trees by:ÃÂ  Jerzy Marcinkowski, Leszek Pacholski v. 119 i. 1-3 p. 19 - 59 Apartness spaces as a framework for constructive topology by:ÃÂ  Douglas S. Bridges, Luminita Dediu v. 119 i. 1-3 p. 61 - 83 Delta20 - categoricity in Boolean algebras and linear orderings by:ÃÂ  Charles F. D. McCoy v. 119 i. 1-3 p. 85 - 120

2 Klaus AmbosSpies, AndrÃ© Nies The Theory of the Polynomial Many-One degrees of Recursive sets is Undecidable. STACS 1992 209-218
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/n/Nies:Andr=eacute=.ht
 List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... Pavel Semukhin : Finite Automata Presentable Abelian Groups. LFCS 2007 EE Bakhadyr Khoussainov Sasha Rubin ... Frank Stephan : Automatic Structures: Richness and Limitations CoRR abs/cs/0703064 EE Wolfgang Merkle Joseph S. Miller ... Frank Stephan : Kolmogorov-Loveland randomness and stochasticity. Ann. Pure Appl. Logic 138 EE Santiago Figueira Frank Stephan : Lowness Properties and Approximations of the Jump. Electr. Notes Theor. Comput. Sci. 143 EE Wolfgang Merkle Joseph S. Miller ... Frank Stephan : Kolmogorov-Loveland Randomness and Stochasticity. STACS 2005 EE Frank Stephan : Lowness for the Class of Schnorr Random Reals. SIAM J. Comput. 35 EE Bakhadyr Khoussainov Sasha Rubin ... Frank Stephan : Automatic Structures: Richness and Limitations. LICS 2004 EE Electr. Notes Theor. Comput. Sci. 84 EE ... Frank Stephan : Trivial Reals. Electr. Notes Theor. Comput. Sci. 66 EE Rodney G. Downey Denis R. Hirschfeldt ... Douglas A. Cenzer Classes. J. Symb. Log. 66 Rodney G. Downey J. Comput. Syst. Sci. 60 Andrea Sorbi : Structural Properties and Sigma Enumeration Degrees.

33. Publications - Timothy Hinrichs
Logicians frequently use axiom schemata to encode (potentially infinite) sets of sentences with particular syntactic form. In this paper we examine a
http://logic.stanford.edu/~thinrich/publications.htm
##### Refereed Proceedings
Hinrichs, T. L., Genesereth, M. R. Extensional Reasoning CADE Workshop on Empirically Successful Automated Reasoning in Large Theories (ESARLT) July 2007 Relational databases are one of the most industrially successful applications of logic in computer science, built for handling massive amounts of data. The power of the paradigm is clear both because of its widespread adoption and theoretical analysis. Today, automated theorem provers are not able to take advantage of database query engines and therefore do not routinely leverage that source of power. Extensional Reasoning is an approach to automated theorem proving where the machine automatically translates a logical entailment query into a database, a set of view definitions, and a database query such that the entailment query can be answered by answering the database query. This paper discusses the framework for Extensional Reasoning, describes algorithms that enable a theorem prover to leverage the power of the database in the case of axiomatically complete theories, and discusses theory resolution for handling incomplete theories.
Hinrichs, T. L., Genesereth, M. R.

34. Logic Colloquium 2003
Older results typically showed the two quantifier level decidable and the third undecidable. We examine the situation for the r.e. degrees, the degrees
http://www.helsinki.fi/lc2003/titles.html
Main Awards Registration Accommodation ... ASL
##### Tutorial speakers
Michael Benedikt Model Theory and Complexity Theory
Bell Labs, Lisle, USA.
E-mail: benedikt@research.bell-labs.com ABSTRACT: This tutorial concentrates on links between traditional (infinitary) model theory and complexity theory. We begin with an overview of the classical' connection between complexity theory and finite model theory, giving quickly the basic results of descriptive complexity theory. /We then discuss several ways of generalizing this to take account a fixed infinite background structure. We will start by giving the basics of complexity theory parameterized by a model (algebraic complexity over an arbitrary structure). We then cover results characterizing first-order theories of models via the complexity of query problems (embedded finite model theory). Finally, time permitting, we will look at abstractions of descriptive complexity theory to take into account a background structure. Stevo Todorcevic Set-Theoretic Methods in Ramsey Theory
C.N.R.S. - UMR 7056, Paris, France.

 35. Atlas: Victoria International Conference 2004 - Abstracts The set of Krandom strings has long been known to be undecidable. It is shown that the Turing degrees of Schnorr-random sets are those of Martin-Loefhttp://atlas-conferences.com/cgi-bin/abstract/select/camo-01?session=1

36. Abstracts
Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all
http://www.impan.gov.pl/~kz/Abstracts.html
 8. Undecidability and concatenation pdf We consider the problem stated by Andrzej Grzegorczyk in `Undecidability without arithmetization'' (Studia Logica 79(2005)) whether certain weak theory of concatenation is essentially undecidable. We give a positive answer for this problem. 7. The Intended Model of Arithmetic. An Argument from Tennenbaum's Theorem pdf We present an argument that allows to determine the intended model of arithmetic using some cognitive assumptions and the assumptions on the structure of natural numbers. Those assumptions are as follows: the psychological version of the Church thesis, computability of addition and multiplication and first order induction. We justify the thesis that the notion of natural number is determined by 6. Coprimality in finite models pdf We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard of addition and multiplication on indices of prime numbers. of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004

37. Lawrence S. Moss: Articles
The Undecidability of Iterated Modal Relativization, with Joseph S. Miller Traditional syllogisms involve sentences of the following simple forms All X
http://www.indiana.edu/~iulg/moss/aarticles.htm
 Abstract Data Types Abstract State Machines Coalgebra Grammars ... Situation Theory Abstract Data Types Final Algebras, Cosemicomputable Algebras, and Degrees of Unsolvability , with Jose Meseguer and Joseph A. Goguen. Theoretical Computer Science 110, (1992), 267-302. Also appears in D.H. Pitt, et al (eds.), Conference on Category Theory and Computer Science, Springer LNCS 283, 1987, 158-181. The theme of this paper is the interaction between recursion-theoretic and algebraic properties of abstract data types. We show that any "algebra with semicomputable inequality which has a nonunit computable $V$-behaviour has a final algebra specification by a finite set of equations and possibly using additional function symbols. For any computable algebra there is a finite set of equations specifying it under both the initial and final algebra semantics. All recursively enumerable degrees of unsolvability arise both in final and initial algebras." (My quotes here are not from the paper, but instead from the summary on by H. JÃ¼rgensen on Math Reviews). Generalization of Final Algebra Semantics by Relativization , with Satish R. Thatte. In M. Main, et al (eds.)

38. AUTHOR INDEX
Single matrices for the operations of both types contain two sets of designated values one of possible values (degrees of truth) for the premisses,
http://www.filozof.uni.lodz.pl/bulletin/v331.html
BULLETIN OF THE SECTION OF LOGIC TABLE OF CONTENTS 1. George TOURLAKIS and Francisco KIBEDI, A Modal Extension of First Order Classical Logic, Part II [Abstract] [DVI] 2. Katsumi SASAKI and Shigeo OHAMA, A Sequent System of the Logic R for Rosser Sentences [Abstract] [DVI] 3. Alexej P. PYNKO, Sequential Calculi for Many-valued Logics with Equality Determinant [Abstract] [DVI] 4. F.A.DORIA and N.C.A.da COSTA, On Set Theory as a Foundation for Computer Science [Abstract] [DVI] 5. Szymon FRANKOWSKI, Formalization of a Plausible Inference [Abstract] [DVI] 6. Andrei KOUZNETSOV, Deduction Chains and DC-like Decision Procedure for Guarded Logic [Abstract] [DVI]
##### ABSTRACTS
1. George TOURLAKIS and Francisco KIBEDI, A Modal Extension of First Order Classical Logic, Part II We define the semantics of the modal predicate logic introduced in Part I and prove its soundness and strong completeness with respect to appropriate structures. These semantical tools allow us to give a simple proof that the main conservation requirement articulated in Part I, Section 1, is met as it follows directly from Theorem 5.1 below. Section numbering is consecutive to that of Part I.

39. Let S Be The Set Of All Sets That Don't Contain Themselves. Does S Contain Itsel
The comment by KK in this metafilter thread (the one this sentence is . For instance, the angles of a triangle in a flat plane always add to 180 degrees,
http://www.metafilter.com/44614/Let-S-be-the-set-of-all-sets-that-dont-contain-t
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self-reference

self

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##### Let S be the set of all sets that don't contain themselves. Does S contain itself? August 27, 2005 5:08 AM Subscribe
This link, which you are no longer looking at, will take you to a pretty cool essay.
posted by Citizen Premier (48 comments total)
This is not the first comment of this very good post, which I enjoyed immensely.
posted by iconomy at 5:52 AM on August 27 This is not the second comment where I say something totally inreverent and everybody ignores me. I think this post is qUite good too. (wasn't there a legendary thread in which we did this forever?) posted by wheelieman at 6:15 AM on August 27 I don't have a comment, I just wanted to say how much I enjoyed this link. posted by Jatayu das at 6:19 AM on August 27 By reading this comment, you are not reading Metafilter posted by Dukebloo at 6:25 AM on August 27 I'm not going to mention in what order, numerically-speaking, this fifth comment falls. I'm not going to comment at all, actually. Just wanted to press home the point, once again, that I really enjoyed the link. posted by iconomy at 6:40 AM on August 27 No commenting allowed in this thread.

 40. All About Oscar The theory had the revolutionary aspect of treating infinite sets as Thus, the existence of undecidable sentences in each such theory points out anhttp://www.britannica.com/oscar/print?articleId=109532&fullArticle=true&tocId=24

41. M. E. Szabo: The Collected Works Of Gerhard Gentzen
In this context he constructs an infinite set of sentences that has no . This refers to a small portion of Godel s 1931 paper on Undecidability.
http://mathgate.info/cebrown/notes/szabo.php
The Omega Group TPS A higher-order theorem proving system This page was created and is maintained by Chad E Brown
##### M. E. Szabo. The Collected Works of Gerhard Gentzen . North-Holland Publishing Company, 1969.
Introduction Investigations into Logical Deduction (1934) Introduction: At age 22 in 1932, Gentzen submitted the paper #1: "On the Existence of Independent Axiom Systems for Infinite Sentence Systems." He introduces a system of the propositional calculus as a sequent calculus based on Hertz's work. He modifies Hertz's "syllogism" rule to be Gentzen's "cut" rule. In this context he constructs an infinite set of sentences that has no independent set of axioms. He also shows that all "linear" sentence systems do have an independent axiomatization. Tarski introduced the semantic notion of logical consequence in 1936. Gentzen had developed this idea (for propositional logic) in #1. Gentzen's natural deduction system in #3 [1935, see below] provides a formalization of the notion of consequence in the sense first used by Bolzano (which was introduced by Bolzano over a hundred years earlier and is analogous to Tarski's notion).

42. 2007-08 UCI Catalogue: Social Sciences
Introduction to sentence logic, including truth tables and natural deduction; . 205C Undecidability and Incompleteness (4). Formal theory of effective
http://www.editor.uci.edu/07-08/ss/ss.10.htm
 DEPARTMENT OF LOGIC AND PHILOSOPHY OF SCIENCE 721 Social Science Tower; (949) 824-1520 Jeffrey A. Barrett, Department Chair Graduate Program Courses The Department of Logic and Philosophy of Science (LPS) brings together faculty and students interested in a wide range of topics loosely grouped in the following areas: general philosophy of science; philosophy of the particular sciences; logic, foundations and philosophy of mathematics; and philosophy of mathematics in application. LPS enjoys strong cooperative relations with UCI's Department of Philosophy; in particular, the two units jointly administer a single graduate program which offers the Ph.D. in Philosophy. LPS also has strong interconnections with several science departments, including Mathematics and Physics, as well as the School of Biological Sciences, the Donald Bren School of Information and Computer Sciences, the Departments of Cognitive Sciences and Economics, and the graduate concentration in Mathematical Behavioral Sciences. Graduate Program Faculty Aldo Antonelli: Logic, philosophy of mathematics, history of analytic philosophy

43. Peter Suber, "Non-Standard Logics"
Would it be interesting to make these sets undecidable? Logics that deal with the truth of conditional sentences, particularly in the subjunctive mood.
http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm
 A Bibliography of Non-Standard Logics Peter Suber Philosophy Department Earlham College In the kinds of non-standard logics included, this bibliography aims for completeness, although it has not yet succeeded. In the coverage of any given non-standard logic, it does not at all aim for completeness. Instead it aims to include works suitable as introductions for those who are already familiar with standard first-order logic. Looking at these non-standard logics gives us an indirect, but usefully clear and comprehensive idea of the usually hazy notion of "standardness". In standard first-order logics: Wffs are finite in length (although there may be infinitely many of them). Rules of inference take only finitely many premises. There are only two truth-values, "truth" and "falsehood". Truth-values of given proposition symbols do not change within a given interpretation, only between or across interpretations. All propositional operators and connectives are truth-functional. "p ~p" is provable even if we do not have p or ~p separately; that is, the principle of excluded middle holds.

 44. Godel's Theorem@Everything2.com It proved difficult to construct a theory of sets which outruled such objects . To prove that an undecidable sentence existed, Godel needed to find ahttp://everything2.com/index.pl?node_id=23136

 45. EULER Record Details Of course $\cup$ is definable in ${\cal D}$, but many interesting degreetheoretic results are expressible as $\Sigma_2$-sentences in the language of \${\calhttp://www.emis.de/projects/EULER/detail?ide=1993jocksigm2theuppe&matchno=11&mat

46. George Boolos - Wikipedia, The Free Encyclopedia
1982, Extremely undecidable sentences, Journal of Symbolic Logic 47 191196. 1987c (with Vann McGee), The degree of the set of sentences of
http://en.wikipedia.org/wiki/George_Boolos
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
##### George Boolos
For the 19th-century British mathematical logician of a similar name, see George Boole
George Boolos Born September 4
New York
New York U.S. Died May 27
Cambridge
Massachusetts U.S.
George Stephen Boolos September 4 New York City May 27 ) was a philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology
##### edit Life
Boolos graduated from Princeton University in 1961 with an A.B. in mathematics Oxford University awarded him the B.Phil in 1963. In 1966, he obtained the first Ph.D. in philosophy ever awarded by the Massachusetts Institute of Technology , under the direction of Hilary Putnam . After teaching three years at Columbia University , he returned to MIT in , where he spent the rest of his career until his death from cancer A charismatic speaker well-known for his clarity and wit, he once delivered a lecture (1994a) giving an account of GÂ¶del's second incompleteness theorem , employing only words of one syllable. At the end of his viva

47. ICALP'07: Accepted Papers - Track B
The Undecidability result holds also for the simulation of twolabel BPP processes. . bound on the length of the local sentence in terms of the original.
http://icalp07.ii.uni.wroc.pl/acceptl-trackb.html
ICALP 2007 34th International Colloquium on
Automata, Languages and Programming Colocated with LICS 2007, LC 2007, and PPDP 2007 Overview Call for Papers Program Committee ... Submissions (closed) Accepted papers short list, alphabetic list with abstracts Online proceedings (NEW!) ... Other events in July in WrocÃÂaw
##### List of accepted papers
(In order of appearance)
##### Track B: Logic, Semantics and Theory of Programming
Modular Algorithms for Heterogeneous Modal Logics Lutz SchrÂ¶der and Dirk Pattinson
State-based systems and modal logics for reasoning about them often heterogeneously combine a number of features such as non-determinism and probabilities. Here, we show that the combination of features can be reflected algorithmically and develop modular decision procedures for heterogeneous modal logics. The modularity is achieved by formalising the underlying state-based systems as multi-sorted coalgebras and associating both a logical and an algorithmic description to a number of basic building blocks. Our main result is that logics arising as combinations of these building blocks can be decided in polynomial space provided that this is the case for the components. By instantiating the general framework to concrete cases, we obtain PSPACE decision procedures for a wide variety of structurally different logics, describing e.g. Segala systems and games with uncertain information.

48. FOM: Midwest Model Theory Meeting
Another way to look at this is to look at the Pi0-1 sentence. There is an old theorem of mine about Undecidability in dynamics of semilinear maps that
http://cs.nyu.edu/pipermail/fom/1999-November/003475.html
##### FOM: Midwest Model Theory Meeting
Harvey Friedman friedman at math.ohio-state.edu

49. Abstracts For Publications Of Prof. J. Maurice Rojas
Computational Arithmetic Geometry I sentences Nearly in the Polynomial We consider the averagecase complexity of some otherwise undecidable or open
http://www.math.tamu.edu/~rojas/abstracts.html
##### Abstracts for Maurice 's Mathematical Papers
(You can click HERE to see a list with downloadable files and further bibliographic information, but without abstracts.) New Complexity Bounds for Certain Real Fewnomial Zero Sets, (by Joel Gomez, Andrew Niles, and J. Maurice Rojas) Extremal Real Algebraic Geometry and A-Discriminants (by Alicia Dickenstein, J. Maurice Rojas, Korben Rusek, and Justin Shih) From Quantum to Algebraic Complexity via Sparse Polynomials (by Sean Hallgren, Bjorn Poonen, and J. Maurice Rojas) A deep problem which remains open is the relation between the complexity classes NP and BQP. Toward understanding this question, we present a natural computational problem that (as an underlying parameter is varied) interpolates between these two famous complexity classes.
More precisely, let UNIFEAS_p denote the problem of deciding whether a univariate polynomial f, with integer coefficients, has a p-adic rational root. Also let UNIFEAS_p(m) denote the analogous problem, restricted to sparse polynomials with m or fewer monomial terms. We show that (a) UNIFEAS_p(2) in BQP, (b) UNIFEAS_p in BQP implies that NP is in BQP. Curiously, the natural analogue of UNIFEAS_p over the real numbers is not even known to be NP-complete. Recent results on Carmichael numbers turn out to be useful in our proofs. A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes (by J. Maurice Rojas)

50. Information
Typically, one points to the sentence This statement is unprovable as an leads to a logical contradiction (a formally undecidable proposition?).
http://serendip.brynmawr.edu/local/scisoc/information/1july04.html
##### Information?: An Inquiry
Tuesdays, 9:30-11 am
Science Building, Room 227 Schedule On-line Forum Evolving Resource List For further information contact Paul Grobstein.
##### Discussion Notes 1 July 2004
Participants: Al Albano (Physics), Doug Blank (Computer Science), Peter Brodfuehrer (Biology), Anne Dalke (English, Feminist and Gender Studies), Wil Franklin (Biology), Paul Grobstein (Biology), David Harrison (Linguistics, Swarthmore), Mark Kuperberg (Economics, Swarthmore), Jim Marshall (Computer Science, Pomona/Bryn Mawr), Liz McCormack (Physics), Lisa Meeden (Computer Science, Swarthmore), Eric Raimy (Linguistics, Swarthmore/Trico), Ed Segall (Edge Technical Associates), Jan Trembly (Alumnae Bulletin), George Weaver (Logic/Philosophy) Summary by Paul Grobstein
presentation notes available
Intending to lay a foundation for discussing Chaitin's work on randomness and algorithmic information theory, Jim laid out a sufficiently rich array of material on the history of logic and its connections to computer science (see first five sections of Jim's notes ) to fully occupy the group for this week. The conversation will continue on to Chaitin's work next week.

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