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1. Set Theory Papers Of Andreas R. Blass
Combinatorial Cardinal characteristics of the continuum (to appear as a chapter in the Handbook of Set Theory (ed. M. Foreman, M. Magidor, and A. Kanamori))
Set Theory Papers
Andreas Blass
The papers are listed in reverse chronological order, except that I put two surveys at the beginning to make them easier to find. Nearly Countable Cardinals PostScript or PDF An expository talk, for a general mathematical audience, about cardinal characteristics of the continuum. Combinatorial Cardinal Characteristics of the Continuum (to appear as a chapter in the Handbook of Set Theory (ed. M. Foreman, M. Magidor, and A. Kanamori)) PostScript or PDF This survey of the theory of cardinal characteristics of the continuum is to appear as a chapter in the "Handbook of Set Theory." As the title indicates, I concentrate on the combinatorial characteristics; Tomek Bartoszynski has written a chapter on the category and measure characteristics. Voting Rules for Infinite Sets and Boolean Algebras PDF A voting rule in a Boolean algebra B is an upward closed subset that contains, for each element x in B, exactly one of x and -x. We study several aspects of voting rules, with special attention to their relationship with ultrafilters. In particular, we study the set-theoretic hypothesis that all voting rules in the Boolean algebra of subsets of the natural numbers modulo finite sets are nearly ultrafilters. We define the notion of support of a voting rule and use it to describe voting rules that are, in a sense, as different as possible from ultrafilters. Finally, we consider how much of the axiom of choice is needed to guarantee the existence of voting rules.

2. [math/9407203] Reductions Between Cardinal Characteristics Of The Continuum
Abstract We discuss two general aspects of the theory of Cardinal characteristics of the continuum, especially of proofs of inequalities between such math
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Title: Reductions Between Cardinal Characteristics of the Continuum
Authors: Andreas Blass (Submitted on 12 Jul 1994) Abstract: We discuss two general aspects of the theory of cardinal characteristics of the continuum, especially of proofs of inequalities between such characteristics. The first aspect is to express the essential content of these proofs in a way that makes sense even in models where the inequalities hold trivially (e.g., because the continuum hypothesis holds). For this purpose, we use a Borel version of Vojtas's theory of generalized Galois-Tukey connections. The second aspect is to analyze a sequential structure often found in proofs of inequalities relating one characteristic to the minimum (or maximum) of two others. Vojtas's max-min diagram, abstracted from such situations, can be described in terms of a new, higher-type object in the category of generalized Galois-Tukey connections. It turns out to occur also in other proofs of inequalities where no minimum (or maximum) is mentioned. Subjects: Logic (math.LO)

3. JSTOR Simple Cardinal Characteristics Of The Continuum
Simple Cardinal characteristics of the continuum. Set theory of the reals, edited by Haim Judah, Israel mathematical conference proceedings, vol.<552:SCCOTC>2.0.CO;2-A

4. Review Andreas Blass, Haim Judah, Simple Cardinal Characteristics
Andreas Blass, Haim Judah, Simple Cardinal characteristics of the continuum. Fulltext Access via JSTOR (no additional login). Go to this article in JSTOR
Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options

5. Atlas: Some Cardinal Characteristics And The Stone-Cech Remainder Of The Reals B
I plan to discuss some recent work on Cardinal characteristics of the continuum, mostly by Heike Mildenberger and me (partly joint, partly disjoint).
Atlas home Conferences Abstracts about Atlas SumTopo 2001, Sixteenth Summer Conference on Topology and its Applications
July 18-21, 2001
City College of CUNY
New York, NY, USA Organizers
Ralph Kopperman (City College, CUNY), Susan Andima (CW Post College, LIU), Gerald Itzkowitz (Queens College, CUNY), Prabudh Misra (College of Staten Island, CUNY), Shelly Rothman (CW Post College, LIU), Aaron Todd (Baruch College, CUNY) View Abstracts
Conference Homepage
Some cardinal characteristics and the Stone-Cech remainder of the reals
Andreas Blass
Mathematics Dept., Univ. of Michigan I plan to discuss some recent work on cardinal characteristics of the continuum, mostly by Heike Mildenberger and me (partly joint, partly disjoint). A prominent role is played by the cofinality of the dominating number and by near coherence of ultrafilters. I shall also describe a connection between this work and the remainder in the Stone-Cech compactification of the reals. Date received: May 23, 2001 Atlas Conferences Inc. Document # cagw-78.

6. Transactions Of The American Mathematical Society
MR 89h03081; Bl 2 A. Blass, Simple Cardinal characteristics of the continuum, in Set Theory of the Reals (H. Judah, ed.

ISSN 1088-6850(e) ISSN 0002-9947(p) Previous issue Table of contents Next issue
Articles in press
... Next Article Ultrafilters on -their ideals and their cardinal characteristics Author(s):
Journal: Trans. Amer. Math. Soc.
MSC (1991): Primary 03E05, 03E35
Posted: March 8, 1999
Retrieve article in: PDF DVI PostScript
This article is available free of charge Abstract References Similar articles Additional information Abstract: For a free ultrafilter on we study several cardinal characteristics which describe part of the combinatorial structure of . We provide various consistency results; e.g. we show how to force simultaneously many characters and many -characters. We also investigate two ideals on the Baire space naturally related to and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter. References:
B. Balcar and P. Simon, On minimal -character of points in extremally disconnected compact spaces

7. AMS Special Session
Michigan, Cardinal characteristics and ultrafilters, available Continuous colorings associated with certain characteristics of the continuum.
Modern Methods in Set Theory and General Topology
Special Session at AMS meeeting #936
organized by Winfried Just and Paul J. Szeptycki
AMS meeting #936 will be held October 9-10, 1998 at Wake Forest University in Winston-Salem, North Carolina. For more information about the meeting, see the August 1998 Notices of the AMS, page 932, or click here List of confirmed speakers Name Institution Title of talk Abstract Zoltan Balogh Miami University Strict p-spaces via elementary submodels availabe Tomek Bartoszynski Boise State
University Special sets of reals available Hal Bennett Texas Tech
University Ordered spaces with special dense subsets pdf-file Andreas Blass University of
Michigan Cardinal characteristics and ultrafilters available Mirna Dzamonja University of
East Anglia On universal c-algebras and universal uniform Eberlein compacta, and related problems pdf-file Ilijas Farah York University Ulam stability and pathological submeasures available William Fleissner University of Kansas D-spaces give a new characterization of semistratifiability available Gary Gruenhage Auburn University Countably compact spaces with a small diagonal available Claude Laflamme University of
Calgary Small filters available David Lutzer College of
William and Mary On a problem of Arhangel'skii and Bella Justin Moore University of
Toronto Continuous colorings associated with certain characteristics of the continuum available Peter Nyikos University of
South Carolina Metrizability of hereditarily normal, hereditarily cwH manifolds

8. 03E: Set Theory
For example, the continuum Hypothesis states that the first Cardinal larger 03E17 Cardinal characteristics of the continuum; 03E20 Other classical set
Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields
POINTERS: Texts Software Web links Selected topics here
03E: Set theory
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. PlanetMath: Cardinality Of The Continuum
This is version 12 of Cardinality of the continuum, born on 200403-15, and foundations Set theory Cardinal characteristics of the continuum)
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Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About cardinality of the continuum (Definition) The cardinality of the continuum , often denoted by , is the cardinality of the set of real numbers . A set of cardinality is said to have continuum many elements. Cantor's diagonal argument shows that is uncountable . Furthermore, it can be shown that is equinumerous with the power set of , so . It can also be shown that has uncountable cofinality Many properties of are independent of ZFC , that is, they can neither be proved nor disproved in ZFC, assuming that ZF is consistent . For example, for every nonzero natural number , the equality is independent of ZFC. (The case is the well-known Continuum Hypothesis .) The same is true for most other alephs , although in some cases equality can be ruled out on the grounds of cofinality, e.g.

10. IngentaConnect Continuous Colorings Associated With Certain Characteristics Of T
Continuous colorings associated with certain characteristics of the continuum of reals associated with various Cardinal invariants of the continuum.

11. List For KWIC List Of MSC2000 Phrases
Cardinal characteristics of the continuum 03E17 Cardinal functions and inequalities, discrete subsets) Cardinality properties ( 54A25 Cardinal numbers
calculus # integral transforms, operational 44-XX
calculus # one-variable
calculus # quantum stochastic
calculus # stochastic calculus of variations and the Malliavin
calculus # umbral
calculus (e.g.: curve sketching, extremum problems) # differential
calculus and other discrete methods # lattice gravity, Regge
calculus and related topics # $q$-
calculus and the teaching of calculus # comprehensive works on
calculus in topological algebras # functional
calculus of functions on infinite-dimensional spaces calculus of functions taking values in infinite-dimensional spaces calculus of Mikusinski and other operational calculi calculus of variations and optimal control; optimization 49-XX calculus of variations and the Malliavin calculus # stochastic calculus of vector functions calculus on manifolds; nonlinear operators calculus, BCK and BCI logics) # substructural logics (including relevance, entailment, linear logic, Lambek calculus, etc. # analytical theory: series, transformations, transforms, operational calculus, etc.) # hermitian and normal operators (spectral measures, functional

12. Handbook Of Set Theory - Mathematical Logic And Foundations Journals, Books & On
continuum. Greg Hjorth, Borel Equivalence Relations , Uri Abraham, Proper Forcing. Andreas Blass, Combinatorial Cardinal characteristics of the continuum

13. The Bulletin Of Symbolic Logic, Volume 8<
A. Blass, Simple Cardinal characteristics of the continuum, reviewed by Heike Mildenberger, page 552. Three papers by B. Balcar, et al., reviewed by Klaas
The Bulletin of Symbolic Logic
Volume 8, 2002
  • The problem of logical constants , by Mario G'omez-Torrente, pages 1 37. Types in logic and mathematics before 1940 , by Fairouz Kamareddine, Twan Laan, and Rob Nederpelt, pages 185 245.
  • Resolution and the origins of structural reasoning: early proof-theoretic ideas of Hertz and Gentzen , by Peter Schroeder-Heister, pages 246 265.
  • Arguments for the continuity principle , by Mark van Atten and Dirk van Dalen, pages 329 347.
  • Provability with finitely many variables , by Robin Hirsch, Ian Hodkinson and Roger D. Maddux, pages 348 379.
  • Some aspects of model theory and finite structures , by Eric Rosen, pages 380 403.
  • Hyperclassical logic (a.k.a. IF logic) and its implications for logical theory , by Jaakko Hintikka, pages 404 423.
  • Computability-theoretic complexity of countable structures
  • Zermelo's Cantorian theory of systems of infinitely long propositions
  • Groups and algebras of nary relations , by Steven Givantt and Hajnal Andr'eka, pages 38 64. Fixed point logics , by Anuj Dawar and Yuri Gurevich, pages 65 88.
  • 14. 03Exx
    03E10, Ordinal and Cardinal numbers. 03E15, Descriptive set theory See also 28A05, 54H05. 03E17, Cardinal characteristics of the continuum
    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

    15. Program Annoucement For ASL Annual Meeting
    Session 910 940 113 Maria Luisa Bonet On Finding Hard Tautologies for Frege Systems 121 Andreas Blass Some Cardinal characteristics of the continuum
    [Prev] [Next] [Index] [Thread]
    Program Annoucement for ASL Annual Meeting

    16. Work By Heike Mildenberger
    A wellknown example for this and this is the continuum hypothesis. Contributions to the Theory of Cardinal characteristics, Habilitationsschrift,
    Welcome to the homepage of
    Priv.-Doz. Dipl.-Math. Dr.

    Heike Mildenberger
    , Austria
    Tel.: +43 (0)1 4277 50517
    Fax.: +43 (0)1 4277 50599
    Email: heike at
    Office no. 90 in the Josephinum
    I studied mathematics and physics in the School of Mathematics and Physics of the . Then I continued in the Section of Mathematical Logic of the Institute of Mathematics , where I received my Ph.D. Then I became an assistant at the University of Bonn, I was a member of the Logic Group in the Mathematical Institute of the University of Bonn, where I finished my habilitation in 1998. I spent two years at Mathematics Department of the The University of Michigan in Ann Arbor , Michigan, holding a fellowship from the Deutsche Forschungsgemeinschaft From April 1999 to March 2001 I was a Minerva fellow at the Institute of Mathematics of the Hebrew University in Jerusalem . Now I am working at the of the University of Vienna . Do you worry about Israel? Clicking at the icon will open the site of "courage to refuse" in English or in Hebrew. Research - very brief form My research area is set theory, mainly infinite combinatorics. Working on a question "is this and this true?" in this area, you have to reckon with

    17. HeiDOK
    03E17 Cardinal characteristics of the continuum ( 0 Dok. ) 03E20 Other classical set theory (including functions, relations, and set algebra) ( 0 Dok.

    18. Springer Online Reference Works
    Cardinal characteristics are also called Cardinal invariants. . always ? turns out to be related to the Suslin conjecture and the continuum hypothesis.

    Encyclopaedia of Mathematics
    Article referred from
    Article refers to
    Cardinal characteristic
    of a topological space A function associating an infinite cardinal number to each space and taking the same value on homeomorphic spaces. Cardinal characteristics are also called cardinal invariants . The domain of definition of a cardinal invariant is the class of all topological spaces or some subclass of it. The following cardinal invariants arose at the first stage of development of general topology. Let be an arbitrary topological space. A trivial invariant is its cardinality , i.e. the cardinality of the set of all its points. Its weight is the smallest cardinality of a base of . The density is the smallest cardinality of a dense subset of . The Suslin number is the least infinite cardinal number such that the cardinality of every family of pairwise-disjoint non-empty open sets does not exceed is the least infinite cardinal number such that every open covering of has a subcovering of cardinality ); a compact Hausdorff space is metrizable if and only if its weight is countable; the Suslin number of the space

    19. MathNet-Mathematical Subject Classification
    03E17, Cardinal characteristics of the continuum. 03E20, Other classical set theory (including functions, relations, and set algebra)

    20. On The Independence Of A Generalized Statement Of Egoroff's Theorem From ZFC, Af
    This independence is easily derived from suitable hypotheses on some Cardinal characteristics of the continuum like b and o, the latter being the least
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    On the independence of a generalized statement of Egoroff's theorem from ZFC, after T.Weiss Authors:

    eprint arXiv:math/0512546 Publication Date:

    ARXIV Keywords:
    Mathematics - Logic, 03E17 (primary), 28A20 (secondary) Comment:
    6 pages Bibliographic Code:
    We consider a generalized version (GES) of the wellknown Severini-Egoroff theorem in real analysis, first shown to be undecidable in ZFC by Tomasz Weiss. This independence is easily derived from suitable hypotheses on some cardinal characteristics of the continuum like b and o, the latter being the least cardinality of a subset of [0,1] having full outer measure. Bibtex entry for this abstract Preferred format for this abstract (see Preferences
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    21. Tarski 100
    Some Cardinal characteristics of the continuum, Andrzej Salwicki Tarski s semantics in software verification(joint work with G. Mirkowska, M. Srebrny,
    Programme of
    the Tarski Centenary Conference
    Monday, 28 May
    Morning session
    Mathematical Institute, 8, Sniadeckich street, 4th floor, room 403
    Opening John W. Addison Jr., Tarski's theory of definability:
    common themes in descriptive set theory, recursive function theory, classical
    pure logic, and finite-universe logic. break
    Solomon Feferman, Tarski's conception of logic
    Afternoon sessions
    Mathematical Institute Banach Centre room 403A
    (Truth and semantics) room 403B
    (Foundations of mathematics) room 13
    (Philosophical logic) room 14
    (Algebra) Vladimir L. Vasyukov Developing Tarski: a Brouwerian
    Topos of Theories
    Angus Macintyre
    Quantifier elimination in geometrical situations, from real closed fields to rigid analytic spaces Janusz Czelakowski,
    Abstract algebraic logic and hierarchies of deductive systems Mai Gehrke Canonical extensions of bounded distributive lattice expansions Mario Gomez-Torrente Reading the "Wahrheitsbegriff" Ludomir Newelski Small profinite structures Don Pigozzi Abstract Algebraic Logic and the Specification of Abstract Data Types break break break break Arianna Betti Lesniewski's Early Solution to the Liar and Tarski Lev Beklemishev Provability algebras and proof-theoretic ordinals Leo Esakia Recent observations concerning Tarski's topological interpretation of the Intuitionistic Calculus Matt Valeriote Decidable Equationally Defined Classes 18:00 Reception by the Rector of Warsaw University ( at Palac Kazimierzowski
    Alfred Tarski memory session
    19:30, Warsaw University, 26/28 Krakowskie Przedmiescie street, Palac Kazimierzowski, Senate Hall

    22. Topology News - November 2005
    Combinatorial Cardinal characteristics of the continuum; Selective screenability and covering dimension; Covering properties of topological spaces.
    Topology Atlas Document # iaal-12
    Topology News
    November 2005
    Topology News Index Topology Atlas

    23. Handbook Of Set Theory
    Combinatorial Cardinal characteristics of the continuum Andreas Blass Invariants of Measure and Category Tomek Bartoszynski
    Unofficial index of online chapters in Handbook of Set Theory (Eds. Foreman, Kanamori Magidor Volume I Chapter name Author(s) Combinatorics Stationary sets Thomas Jech Partition Relations ... Todorcevic Ramsey Theory for Banach Spaces Stevo Todorcevic Continuum Borel equivalence relations Greg Hjorth ... Bartoszynski Revised countable support iterations Hans-Dieter Donder , Ulrich Fuchs Constructibility Constructibility and Class Forcing Sy D. Friedman ... Philip Welch Volume II Chapter name Author(s) Elementary Embeddings Elementary embeddings and algebra Patrick Dehornoy Iterated Forcing and Elementary Embeddings James Cummings Ideals and Generic Elementary Embeddings Matthew Foreman Singular Cardinals Cardinal Arithmetic Uri Abraham Menachem Magidor Prikry -type Forcings Moti ... Eisworth Volume III Chapter name Author(s) Inner Model Theory Beginning Inner Model Theory William J. Mitchell The Covering Lemma William J. Mitchell ... Schimmerling Determinacy Structural Consequences of AD Stephen C. Jackson Determinacy in L(R) Itay ... Neeman Large Cardinals from Determinacy Peter Koellner W. Hugh

    24. Award#0653696 - Logic, Sets, Categories, And Applications
    Such an extension is useful for the theory of Cardinal characteristics of the continuum. Borel functions at the base type (real numbers) already play a

    25. MSC 2000 : CC = Act
    03E17 Cardinal characteristics of the continuum Nouveau code MSC 2000 .. 76XX Fluid mechanics For general continuum mechanics, see 74Axx,

    26. Bulletin Of Symbolic Logic, 2002; 8 (4)
    REVIEWS Simple Cardinal characteristics of the continuum. / Blass, A / Mildenberger, Heike, 552-553. REVIEWS - Three papers / Balcar, B / Hart,
    Sumario Título / Autor(es) Página(s) Computability-theoretic complexity of countable structures / Harizanov, Valentina S Zermelo's Cantorian theory of systems of infinitely long propositions / Taylor, R Gregory REVIEWS - Platonism and anti-platonism in mathematics. / Balaguer, M Leng, Mary REVIEWS - Mathematical intuitionism and intersubjectivity. / Placek, T Horsten, Leon REVIEWS - A short introduction to intuitionistic logic. / Mints, G Schwichtenerg, Helmut REVIEWS - Simple theories. / Wagner, F Hart, Bradd REVIEWS - Introduction to cardinal arithmetic. / Holz, M Steffens, K Weitz, E Burke, Maxim R REVIEWS - Topics in topology. / Todorcevic, S Farah, Ilijas REVIEWS - Parameterized complexity. / Downey, R Fellows, M Flum, Jörg REVIEWS - The p-calculus. / Sangiorgi, D Walker, D Hüttel, Hans REVIEWS - The structure of values and norms. / Hansson, S Bailhache, Patrice REVIEWS - Fragments of Heyting arithmetic. / Burr, W Beklemishev, Lev REVIEWS - Two papers - Explicit mathematics. / Strahm, T Cantini, A Ferreira, Fernando REVIEWS - First steps into metapredicativity in explicit mathematics. / Strahm, T

    27. Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical Logic A
    edit 03E17 Cardinal characteristics of the continuum .. PM proof of \Diamond is equivalent to \clubsuit and continuum hypothesis, id=3248 WP guess
    var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
    Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical logic and foundations
    From Wikipedia, the free encyclopedia
    Wikipedia:WikiProject Mathematics PlanetMath Exchange Jump to: navigation search This page provides a list of all articles available at PlanetMath in the following topic:
    03-XX Mathematical logic and foundations
    This list will be periodically updated. Each entry in the list has three fields:
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    28. List KWIC DDC And MSC Lexical Connection
    continuum Cardinal characteristics of the 03E17 continuum hypothesis and Martin s axiom 03E50 continuum limits 81T27 continuum models (systems of
    conjecture # L$-functions of varieties over global fields; Birch - Swinnerton - Dyer
    conjecture, etc.) # isomorphism problems (reconstruction
    conjectures (intersection theorems) # homological
    conjectures, nonabelian class field theory # Langlands - Weil
    conjectures, nonabelian class field theory # Langlands - Weil
    conjugacy classes
    conjugate functions, conjugate series, singular integrals
    connected and locally connected spaces (general aspects)
    connected spaces (general aspects) # connected and locally
    connected with nontransversal intersection # bifurcations
    connectedness # higher-dimensional local connection problems (linear and nonlinear) # Stokes phenomena and connection with control problems # PDE in connection with logical questions # automata and formal grammars in connection with modular forms # Dirichlet series and functional equations in connections # linear and affine connections # other connections # projective connections and metrics on vector bundles (Hermite - Einstein - Yang - Mills) # special connections of semigroups with homological algebra and category theory connections with differential equations connections with differential equations connections with groups, algebras, and related topics

    29. FMHSRN - Letter 2
    They exist along a continuum, however, from more rural to less rural and vary . geographic areassome of the Cardinal characteristics of a rural area.
    Focusing on "Frontier": Isolated Rural America
    Letter to the Field No. 2
    by James A. Ciarlo, PhD, John H. Wackwitz, PhD, Morton O. Wagenfeld, PhD, Dennis F. Mohatt, MA
    Compiled by Pearlanne T. Zelarney, MS
    Frontier Mental Health Services Resource Network
    Last revised: 4/11/96
    Table of Contents
    Defining Rural Areas Alternative Typologies of "Rural" Future Work on Rural Area Definitions ... References
    The word "frontier" itself conjures up a special set of images for most of us. Indeed, historians (e.g., Turner, 1993; Webb, 1952) have argued the frontier shaped American character. One associates the frontier with such terms as pioneers, hunters, trappers, ranchers, and Indians. While the frontier of historic imagination no longer exists, the frontier does live on in the western US and Alaska. It is protected from large-scale settlement by harsh climate, difficult terrain, lack of water, distance from metropolitan areas, lack of exploitable resources, and various access restrictions on large federal land tracts (Duncan, 1993; Popper, 1986). As one might expect, providing any type of human services to this rural population presents formidable geographic, cultural, and human resource problems. Back to Table of Contents
    Defining Rural Areas
    As the following sections will discuss, distinguishing frontier rural areas from other "rural" areas in research and literature can also be a challenge. Rural areas share the common characteristics of comparatively few people living in the area, limited access to large cities (and sometimes even to smaller towns), and considerable traveling distances to "market areas" for either work or everyday-living activities. They exist along a continuum, however, from more rural to less rural and vary extensively based on the following factors (Hewitt, 1989):

    30. Fields Institute - Set Theory Seminars
    We apply it to show that there are continuummany (in fact, This time we will make emphasis on Cardinal characteristics of semifilters (for details,
    Home About Us NPCDS/PNSDC Mathematics Education ... Search
    December 24, 2007
    Set Theory Seminars
    The Fields Institute currently hosts an ongoing Set Theory seminar series, meeting each Friday at 1:30 p.m.
    Ilijas Farah
    York University, Juris Steprans , York University 2002 Thematic Program on Set Theory and Analysis.
    Seminars held during 2002-03
    Seminars held during 2003-04
    June 24, 2005
    Maxim R. Burke , UPEI
    Liftings for category algebras
    June 17, 2005
    Juris Steprans , York University
    A regular CLP-compact space of countable tightness whose square is not CLP-compact June 10, 2005
    Ilijas Farah , York University
    Prikry problem for Suslin forcings June 3, 2005, 1:30-3:00pm Stevo Todorcevic Representing Trees as Relatively Compact subsets of the first Baire Class May 13, 2005, 1:30-3:00 pm, Room 210 Dikran Dikranjan , York University and University of Udine Characterizing subgroups of the circle and of the compact abelian groups April 22, 2005, 1:30-3:00 pm, Room 210

    31. UpToDate Sepsis And The Systemic Inflammatory Response Syndrome: Definitions, Ep
    continuum of severity characteristics THAT INFLUENCE OUTCOME In this syndrome, tissues remote from the original insult display the Cardinal signs of

    32. Publications And Talks
    continuum methods of physical modelling – continuum mechanics, .. Coupling of simulated physical Cardinal characteristics with observed phytoplankton
    Hutter, K., Jöhnk, K.D., 2004. Springer-Verlag, Berlin Heidelberg, pp. 635.
    Publications in press Verspagen, J.M.H., Passarge, J., Jöhnk, K.D., Visser, P.M., Peperzak, L., Boerse, P., Laanbroek, H.J. and Huisman, J., 2005. Water management strategies against toxic Microcystis blooms in the Dutch delta. Ecological Applications. Reviewed publications Verspagen, J.M.H., Snelder, E.O.F.M., Visser, P.M., Jöhnk, K.D., Ibelings, B.W., Mur, L.R., Huisman, J., 2005. Benthic - pelagic coupling in the population dynamics of the cyanobacterium Microcystis . Freshwater Biology 50: 854-867. Ostendorp, W., Schmieder, K., Jöhnk, K.D., 2004. Assessment of human pressures and hydromorphological impacts on lakeshores in Europe. Ecohydrology and Hydrobiology 4: 379-395. Schmieder, K., Dienst, M., Ostendorp, W., Jöhnk, K.D., 2004. Effects of water level variations on the dynamics of the reed belts of Lake Constance. Ecohydrology and Hydrobiology 4: 469-480. Jöhnk, K.D., Straile, D., Ostendorp, W., 2004. Extreme Floods at Lake Constance - Climate impact on lake shore biocoenosis in the light of the 1999 centennial flood. Limnologica 34: 15-21.

    Further we introduce an ordering on the set of partitionfilters and consider the dual form of some Cardinal characteristics of the continuum.
    FUNDAMENTA MATHEMATICAE ISSN: 0016-2736(p) 1730-6329(e)
    Ramseyan ultrafilters
    Lorenz Halbeisen
    Fund. Math.
    MSC (2000): Primary 05D05, 05D10; Secondary 03E05, 03E40, 03E17, 03E35.
    Retrieve article in PDF
    (191.09 Kb)
  • Department of Pure Mathematics
    Queen's University Belfast
    Belfast BT7 1NN, Northern Ireland
  • 34. Set Theory (Springer Monographs In Mathematics): ‹IˆÉš ‰®‘“XBookWeb
    Translate this page These methods have been applied to combinatorial set theory, Cardinal characteristics of the continuum, descriptive set theory, the singular Cardinal
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      Set Theory (Springer Monographs in Mathematics) -DE-
      ISBN:9783540440857 (Hard cover book)
      3rd, rev. Edition
      Jech, Thomas
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    35. DBLP: Saharon Shelah
    Saharon Shelah Strongly meager sets of size continuum. 162 Heike Mildenberger, Saharon Shelah Changing Cardinal characteristics without changing
    Saharon Shelah
    List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... Heike Mildenberger , Saharon Shelah: Increasing the groupwise density number by c.c.c. forcing. Ann. Pure Appl. Logic 149 EE Andrzej Roslanowski , Saharon Shelah: Universal forcing notions and ideals. Arch. Math. Log. 46 EE Gregory L. Cherlin , Saharon Shelah: Universal graphs with a forbidden subtree. J. Comb. Theory, Ser. B 97 EE Chanoch Havlin , Saharon Shelah: Existence of EF-equivalent non-isomorphic models. Math. Log. Q. 53 EE Shimon Garti Math. Log. Q. 53 ... Mirna Dzamonja , Saharon Shelah: On properties of theories which preclude the existence of universal models. Ann. Pure Appl. Logic 139 EE Saharon Shelah: More on the revised GCH and the black box. Ann. Pure Appl. Logic 140 EE Heike Mildenberger , Saharon Shelah, Boaz Tsaban : Covering the Baire space by families which are not finitely dominating. Ann. Pure Appl. Logic 140 EE Noam Greenberg , Saharon Shelah: Models of real-valued measurability. Ann. Pure Appl. Logic 142

    36. Fall 2003 Departmental News
    Jason’s research interests are in set theory, more specifically Cardinal characteristics of the continuum, set theoretic topology, and applications ot
    Fall 2003 Departmental News
    Return to Fall 2003 Newsletter Central College Mount Mercy College Clarke College ... The Franciscan University (formerly Mount St. Claire College) Cornell College University of Iowa Mathematics Department Grinnell College University of Northern Iowa ... Wartburg College Central College
    Mark Mills
    We have begun this school year in the renovated and expanded Vermeer Science Center. The project cost $20 million, and it tripled the size of the building. We now have a number of new computer labs, and there are instructor computers and projectors in each classroom. The transition to the new space has really gone quite smoothly. We hope you will come to the section meeting in April to see our new building. Our computer science colleague Robert Franks recently received a CSEMS grant of $315,000 from NSF to be used for scholarships. The goal of the grant is to increase the number of mathematics and computer science majors here. This year's freshman class is the first to receive the scholarships. Central College is now a part of the AQIP process for accreditation. One of the three major campus initiatives under AQIP is to increase the number of mathematics and science majors who pursue secondary licensure.

    37. Afrikanistik Online - Cardinal Directions And Environmental Concepts Of Landscap
    is frequently perceived as a continuum. In order to specify the semantic the characteristics of landscape according to the regional qualities of the
    @import url(; @import url(; @import url(; @import url(;
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    Direkt zum Inhalt Sektionen Suchen Inhalt
    1. 1. Introduction 2. 2. The position of Kwanyama within the Owambo dialect cluster 3. 3. Cardinal directions 4. 4. Forest areas and seasonal grasslands ... Cardinal directions and environmental concepts of landscape in Kwanyama Nachrichten Rezensionsangebot - Book for review Neuer Beitrag Neuer Beitrag Beitragsank¼ndigung / forthcoming contribution (10.2007) Neue Rezensionsangebote (Okt 2007) Mehr ...
    Cardinal directions and environmental concepts of landscape in Kwanyama (Owambo) Dirk Otten urn:nbn:de:0009-10-2491
    1. Introduction
    This contribution examines some conceptual domains of environment among the Kwanyama speakers of northern Namibia, focussing on the linguistic expression as well as on their semantic facets and richness. In many cases, it will become clear that the designation of landscape and its scenic characteristics of landscape does not necessarily require specific terms. Instead, it often makes use of phraseological and descriptive devices, which must be regarded as strongly context dependent. The major part of this paper deals with different types of landscape, their conceptualisation as well as their linguistic expression. This includes mainly the domains of forest, savannah, seasonal grassland and their salient features and elements. Finally, the findings will be contrasted with results from my survey on place names conducted in the Owambo region as part of a

    38. NOTES For Week 9
    are part of a continuum described in older books as under nutrition. observed in every developing country and has three Cardinal characteristics for Week 9.htm
    NOTES for Week 9 I. PHEROMONES The alleged sensor in humans is the vomeronasal organ (VNO) found in the nose. People who insist that human pheromones are significant say that when humans began wearing clothes, pheromones lost their importance. According to Martha McClintock at the University of Chicago, the 'sixth sense' human pheromones do exist. These substances have been well documented in insects and many mammals. In those animals, pheromones do such things as block pregnancies, influence mating, identify territory, and influence the timing of puberty and dominance. McClintock has pursued pheromones for thirty years. She gained fame in 1971 when-as an undergraduate-documented that 135 women in her dormitory coordinated their menstrual cycles. The phenomenon is called menstrual synchrony The possible medical implications are possible tools for regulating ovulation in couples having conception difficulty, alleviation of depression, and management of prostate problems in men. ..... CJ '99 Resources Bishop, J. "Sixth-Sense Therapy Path to Be Reported"

    39. What Is A Commodity? Two Axiomatic Answers*. - Journal, Magazine, Article, Perio
    Euclidean) space of characteristics and thus form a continuum. The concept of Cardinal commodity is extremely useful it gives meaning to unit
    We have detected that your web browser does not have JavaScript enabled. To view Goliath's company profiles, news and business information, please enable JavaScript now. var tcdacmd="dt"; About Us My Account No items in your cart Select a Category Online Courses Business Encyclopedias Business News Company Profiles Business Plans Find Articles by Publication What is a commodity? Two axiomatic answers*. Publication Date: 01-JAN-04 Publication Title: Economic Theory
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    Description Summary. We identify conditions under which preferences over subsets of a consumption world can be reduced to preferences over bundles of "commodities". We distinguish ordinal bundles, whose coordinates are defined up to monotone transformations, from cardinal bundles, whose coordinates are defined up to positive linear transformations. Keywords and Phrases: Commodity, Preference, Ordinal measure, Cardinal measure. JEL Classification Numbers: D11. 1 Introduction This note is an attempt to endogenize the notion of commodity. According to the standard view in economic theory, spelled out in Debreu (1959) for instance, a commodity is defined by specifying the objective, intrinsic characteristics it possesses. This includes not only its physical attributes, but also the location, time, and state of the world at which it is available. In Debreu's model, commodities are completely homogenous and finite in number. In Lancaster's framework, or in its refinements such as Mas-Colell's model, characteristics remain exogenously defined, objective, and measurable in a cardinal sense. Here we take one further step towards endogenizing commodities. Most economic theorists would consider that if two goods are perfect substitutes in the eyes of all economic agents, it is parsimonious and useful modelling practice not to distinguish between them, even if they are intrinsically quite different. Conversely, advertisers often work hard to emphasize product differences that are intrinsically trivial. These casual observations suggest that commodities should perhaps be given a subjective and collective definition: what matters to define a commodity is probably not as much the objective characteristics of it as the ones subjectively perceived and considered relevant by all agents.

    40. Cardinal Curriculum Level 2
    Identify the characteristics that distinguish a Gift from a Sponsored Project Project Indicators continuum and Determination Process Checklist
    Cardinal Curriculum Level II Certification Contact Us Home STARS
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    At Stanford Online Class Test Gift Administration Website Glossary Gift Administration at Stanford
    ORA-1128 Class Content Gift Administration at Stanford is an online class that addresses the responsibilities involved in administering gifts of cash in the form of checks and wire transfers as well as property. The class is appropriate for staff and faculty who administer gifts. The class is divided into six modules.
  • Gifts are Important to Stanford Overview of Gift Administration Policy, Fundamentals, and Responsibilities Determine Whether Funds Can Be Classified as a Gift, or Support for a Sponsored Project Gift Processing Tasks
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  • 41. Britannica Online Encyclopedia
    Cardinal number. (from the article continuum hypothesis ) key result in starting set transducer ) Microphones also have directional characteristics.
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    (from the article "cardinal") The cardinal bishops are the successors of the bishops of the sees just outside Rome. There were seven of these sees in the 8th century, but the ... cardinal camerlengo (from the article "conclave") Upon the death of a pope, the cardinal camerlengo, the personal representative of the Sacred College of Cardinals in the administration of the ... cardinal deacon cardinal fish any fish of the family Apogonidae (order Perciformes), a group including about 200 species of small, typically nocturnal fishes found in tropical ... [1 related articles] cardinal flower any of several closely related species of the genus Lobelia, perennial plants of the family Lobeliaceae that are native to North and Central ...

    42. 358/369 (Total 5522) NO 167 03E65 Other Hypotheses
    Translate this page 156, 03E17, Cardinal characteristics of the continuum. 155, 03E15, Descriptive set theory See also 28A05, 54H05. 154, 03E10, Ordinal and Cardinal numbers

    43. Schiller Institute—The Truth About Temporal Eternity
    and the fact that the metrical characteristics of a continuum can only be Cardinal Nicolaus of Cusa, De Docta Ignorantia (On Learned Ignorance),
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    The Truth About Temporal Eternity
    Appendix I and II
    Lyndon H. LaRouche, Jr.
    March 14, 1994
    Part 1 (of 3)
    This article is reprinted from the Summer, 1 994 issue of FIDELIO Magazine
    Appendix A ... Vol 3, No 2
    Appendix A:
    The Ontological Superiorityof Nicolaus of Cusa's Solution
    Over Archimedes' Notion of Quadrature
    by Lyndon H. LaRouche, Jr.
    Archimedes' theorems for quadrature of the circle are given in The Works of Archimedes , T. L. Heath, ed., Dover, New York, pps. 91-98, 233-252, and also conveniently referenced in Ivor Thomas, trans., Greek Mathematical Works I. "Thales to Euclid," Loeb Classical Library , No. 335 (1939), 1980, pp. 316-333 of Section IX.2., pp. 308-346. The kernel of Archimedes' construction is given in the two diagrams in the latter work., on pp. 318, 319, respectively. For our purposes here, consider the entirety of pp. 308-346 as the relevant portion of the background against which this appended note is written. The issue addressed here, will almost certainly prove to have been the principal, putatively scientific objection to our portrait of Nicolaus of Cusa's reformulation of Archimedes' quadrature of the circle. We shall focus narrowly upon that ontological point of difference between Cusa's and Archimedes' constructions which defines Cusa and his radiated influence, on the point of this single crucial issue, as the initiator of all progress in mathematical science over the interval A.D. 1440-1897, and beyond. Our proof of this point is very elementary, indeed, but we believe also rigorous.

    44. Project MUSE
    Keeping these characteristics in mind and also critically pondering the degrees pragmatism provides the common thread that connects this continuum all
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    Performing Live: Aesthetic Alternatives for the Ends of Art (review)
    Philosophy of Music Education Review - Volume 12, Number 1, Spring 2004, pp. 89-93
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    45. List Of External References. %% (Includes All Entries From The
    title = {{Combinatorial Cardinal characteristics of the continuum}}, Cardinals and a strong form of the negation of the generalized continuum

    46. Adult Mammalian Forebrain Ependymal And Subependymal Cells Demonstrate Prolifera
    of the Cardinal characteristics of stem cells, the ability to selfrenew. Ventricular Zone (VZ) a continuum of the Neural Stem Cell Compartment

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    Adult Mammalian Forebrain Ependymal and Subependymal Cells Demonstrate Proliferative Potential, but only Subependymal Cells Have Neural Stem Cell Characteristics
    Bernard J. Chiasson, Vincent Tropepe, Cindi M. Morshead, and Derek van der Kooy Neurobiology Research Group, Department of Anatomy and Cell Biology, University of Toronto, Toronto, Canada, M5S 1A8

    47. Increased Psychological Distress Among Danish Gulf War Veterans Without Evidence
    The Cardinal characteristics of projective thought, hostility, suspiciousness, The psychoticism scale provides a graduated continuum from mild
    Danish Medical Bulletin - No. 1. February 2004. Vol. 51 Pages 108-13.
    Increased psychological distress among Danish gulf war veterans - without evidence for a neurotoxic background
    The Danish Gulf War Study , Joachim Knop
    cand.odont. Poul Suadicani , Bernadette Guldager , research Merete Appleyard
    Finn Gyntelberg PDF 1) Epidemiological Research Unit, Clinic of Occupational and Environmental Medicine, H:S Copenhagen University Hospital, DK-2400 Copenhagen. 2) The Danish Armed Forces Health Services, DK-2820 Gentofte. 3) Institute of Preventive Medicine, H:S Copenhagen University Hospital, DK-1399 Copenhagen. Correspondence: Epidemiological Research Unit, Clinic of Occupational and Environmental Medicine, H:S Copenhagen University Hospital, Bispebjerg, Bispebjerg Bakke 23, DK-2400, Copenhagen.
    Introduction.: Compared with controls, up to six years after their return, Danish Gulf War veterans have a significantly higher prevalence of self-reported neuropsychological symptoms, potentially as a result of neurotoxic exposure during deployment. We tested the hypotheses that: 1) GW veterans would perform less well than controls using a computerized neuromotor test battery; and that 2) GW veterans have a psychological profile different from that of controls. Material and methods: Results.:

    48. Achilles And The Tortoise, Part 2
    It is transfinite and of the order of the Cardinal number c. . challenged to define the basic characteristics of the four dimensional continuum of Space
    ACHILLES AND THE TORTOISE by GOTTHARD GÜNTHER Relativity shows that nothing can move in space faster than light. The interstellar cruiser becomes possible only if we can, somehow, transcend that limitation. And one way may be simply that of asking, and finding a new answer, to the deeply fundamental question, "What do you mean by ´motion´?" - part 2 of 3 - The solution of a riddle or of a paradox is usually something in the nature of an anticlimax. The suspension is released, and the feeling of exciting wondermemt has passed. A famous. example is the story of the Gordian knot. When Alexander the Great conquered Asia he found in the city of Gordius an old chariot its yoke fastened with a cord that was tied in a complicated knot. The cord was so artfully twisted that no one had ever been able to loosen it. Moreover, there was an oracular Prophecy that he, who first would untie the knot, should rule Asia. Alexander tried, but he, too, failed. So he took his sword and "untied" the knot by cutting it in two. At this point an intellectually healthy and normal person is very much tempted to say: "So what if we do not understand motion? Newton's and Leibniz's calculus permits us to

    49. Floyd Henry Allport: Floyd H. Allport
    Such a construct was called a telic continuum. . This was true of his notions of personal dispositions; Cardinal characteristics, and congruence in
    A Mead Project source page
    Originally published as:
    Floyd Henry Allport. "Floyd H. Allport." In Gardner Lindzey (ed) A History of Psychology in Autobiography 6. Englewood Cliffs, NJ: Prentice-Hall (1974): 3- 29.
    Editors' notes
    This is Allport's autobiography, long thought to be the only one he left. We accidentally happened across three others, published in class yearbook updates. They provide useful details he later found unimportant.
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    Floyd Henry Allport. "Floyd Henry Allport." Harvard College Class of 1913: Secretary''s Second Report: June 1917 . Norwood, MA: Plimpton Press (1917): 5-6. Floyd Henry Allport. "Floyd Henry Allport." ... . Cambridge, MA: Harvard University Press (1923): 5-6.
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    50. Citebase - Reductions Between Cardinal Characteristics Of The Continuum
    G/A, REDUCTIONS BETWEEN Cardinal characteristics 17 9. J. Pawlikowski, Why Solovay real produces Cohen real, J. Symbolic Logic 51 (1986), 957968.

    51. Phys. Rev. A 36 (1987): Y. C. Yu And G. Lapicki - Deconvolution And Characterist
    Deconvolution and characteristics of cusp spectra for electron transfer to the projectile’s continuum (ETC) Extraction of a generic cross section
    Physical Review Online Archive Physical Review Online Archive AMERICAN PHYSICAL SOCIETY
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    Abstract/title Author: Full Record: Full Text: Title: Abstract: Cited Author: Collaboration: Affiliation: PACS: Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST PER Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article: MyArticles: View Collection Help (Click on the to add an article.)
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    Next article Issue 10 View Page Images PDF (2115 kB), or Buy this Article Use Article Pack Export Citation: BibTeX EndNote (RIS) Deconvolution and characteristics of cusp spectra for electron transfer to the projectile’s continuum (ETC): Extraction of a generic cross section
    Y. C. Yu and G. Lapicki Department of Physics, East Carolina University, Greenville, North Carolina 27858
    Received 21 May 1987 Observed cusp spectra for electron transfer to the continuum (ETC) of 0.6-MeV/u H , He , and He ions from hydrocarbon gaseous targets (CH , C H , and C H ) are fitted to a generic expression of Meckbach, Nemirovsky, and Garibotti [Phys. Rev. A

    52. Mrs. Tomera TeacherWeb Math Continuum
    MATHEMATICS continuum 1. AWARENESS STAGE Rote counts to ten or more but with little understanding Uses concrete objects to represent Cardinal numbers.
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    53. Emerald: Article Request
    fit the model of a university described by Cardinal Newman some 150 years ago . as just an extension of the continuum for some styles of university work,

    54. Catholic World News : Vatican Observatory Head Clashes With Cardinal On Evolutio
    Father Coyne, in his Tablet essay, contradicts the Cardinal s position, may be a few half baked universes floating arround in their own time continuum.

    55. Peter Vojtas, Series And Toeplitz Matrices (a Global Implicit
    File Format Unrecognized View as HTML

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