This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related

Contents
919 found
Order:
1 — 50 / 919
Material to categorize
  1. Physicalistic Platonism.Penelope Maddy - 1990 - In A. D. Irvine (ed.), Physicalism in Mathematics. Dordrecht: Kluwer. pp. 259-290.
    Remove from this list  
     
    Export citation  
     
    Bookmark   10 citations  
  2. Executing Gödel's Programme in Set Theory.Neil Barton - 2017 - Dissertation, Birkbeck, University of London
  3. Nota: ¿CUÁL ES EL CARDINAL DEL CONJUNTO DE LOS NÚMEROS REALES?Franklin Galindo - manuscript
    ¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de Lógica (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  4. Intrinsic Justifications for Large-Cardinal Axioms.Rupert McCallum - 2021 - Philosophia Mathematica 29 (2):195-213.
    ABSTRACT We shall defend three philosophical theses about the extent of intrinsic justification based on various technical results. We shall present a set of theorems which indicate intriguing structural similarities between a family of “weak” reflection principles roughly at the level of those considered by Tait and Koellner and a family of “strong” reflection principles roughly at the level of those of Welch and Roberts, which we claim to lend support to the view that the stronger reflection principles are intrinsically (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  5. Chance and the Continuum Hypothesis.Daniel Hoek - 2021 - Philosophy and Phenomenological Research 103 (3):639-60.
    This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  6. H. J. Keisler and A. Tarski. From accessible to inaccessible cardinals. Fundamenta mathematicae, vol. 53 , pp. 225–308. , p. 119.). [REVIEW]Azriel Lévy - 1967 - Journal of Symbolic Logic 32 (3):411.
  7. Steven Orey. New foundations and the axiom of counting. Duke mathematical journal, vol. 31 (1964), pp. 655–660.Norman Feldman - 1970 - Journal of Symbolic Logic 34 (4):649-649.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  8. A. Lévy and R. M. Solovay. Measurable cardinals and the continuum hypothesis. Israel journal of mathematics, vol. 5 (1967), pp. 234–248. [REVIEW]F. R. Drake - 1970 - Journal of Symbolic Logic 34 (4):654-655.
  9. Takeo Sugihara. The numbers of modalities in T supplemented by the axiom CL 2 pL 3 p. The journal of symbolic logic, vol. 27 no. 4 (for 1962, pub. 1963), pp. 407–408. [REVIEW]Krister Segerberg - 1969 - Journal of Symbolic Logic 34 (2):305-305.
  10. C. C. Chang. Maximal n-disjointed sets and the axiom of choice. Fundamenta mathematicae, vol. 49 , pp. 11–14.Azriel Lévy - 1970 - Journal of Symbolic Logic 35 (3):473.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  11. J. W. Addison and Yiannis N. Moschovakis. Some consequences of the axiom of definable determinateness. Proceedings of the National Academy of Sciences, vol. 59 , pp. 708–712. - Donald A. Martin. The axiom of determinateness and reduction principles in the analytical hierarchy. Bulletin of the American Mathematical Society, vol. 74 , pp. 687–689. [REVIEW]James E. Baumgartner - 1973 - Journal of Symbolic Logic 38 (2):334.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  12. Shaligram Singh. The independence of a strong axiom of choice. The mathematical gazette, vol. 46 , pp. 126–129.H. B. Enderton - 1973 - Journal of Symbolic Logic 38 (2):335.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  13. E. M. Kleinberg. Strong partition properties for infinite cardinals. The journal of symbolic logic, vol. 35 , pp. 410–428.James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (3):463.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  14. Jack H. Silver. Measurable cardinals and well-orderings. Annals of mathematics, ser. 2 vol. 94 , pp. 414–446.Menachem Magidor - 1974 - Journal of Symbolic Logic 39 (2):330-331.
  15. Herman Rubin and Jean E. Rubin. Equivalents of the axiom of choice, II. Studies in logic and the foundations of mathematics, vol. 116. North-Holland, Amsterdam, New York, and Oxford, 1985, xxviii + 322 pp. [REVIEW]David Pincus - 1987 - Journal of Symbolic Logic 52 (3):867-869.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  16. Donald A. Martin and John R. Steel. Projective determinacy. Proceedings of the National Academy of Sciences of the United States of America, vol. 85 , pp. 6582–6586. - W. Hugh Woodin. Supercompact cardinals, sets of reals, and weakly homogeneous trees. Proceedings of the National Academy of Sciences of the United States of America, vol. 85 , pp. 6587–6591. - Donald A. Martin and John R. Steel. A proof of projective determinacy. Journal of the American Mathematical Society, vol. 2 , pp. 71–125. [REVIEW]Matthew D. Foreman - 1992 - Journal of Symbolic Logic 57 (3):1132-1136.
  17. Michiel van Lambalgen. Independence, randomness and the axiom of choice. The journal of symbolic logic, vol. 57 , pp. 1274–1304.John C. Simms - 1994 - Journal of Symbolic Logic 59 (4):1433-1434.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  18. Arthur W. Apter. On the least strongly compact cardinal. Israel journal of mathematics, vol. 35 , pp. 225–233. - Arthur W. Apter. Measurability and degrees of strong compactness. The journal of symbolic logic, vol. 46 , pp. 249–254. - Arthur W. Apter. A note on strong compactness and supercompactness. Bulletin of the London Mathematical Society, vol. 23 , pp. 113–115. - Arthur W. Apter. On the first n strongly compact cardinals. Proceedings of the American Mathematical Society, vol. 123 , pp. 2229–2235. - Arthur W. Apter and Saharon Shelah. On the strong equality between supercompactness and strong compactness.. Transactions of the American Mathematical Society, vol. 349 , pp. 103–128. - Arthur W. Apter and Saharon Shelah. Menas' result is best possible. Ibid., pp. 2007–2034. - Arthur W. Apter. More on the least strongly compact cardinal. Mathematical logic quarterly, vol. 43 , pp. 427–430. - Arthur W. Apter. Laver indestructibility and the class of compact cardinals. The journal of sy. [REVIEW]James W. Cummings - 2000 - Bulletin of Symbolic Logic 6 (1):86-89.
  19. William Mitchell, Ernest Schimmerling, and John Steel. The covering lemma up to a Woodin cardinal. Annals of Pure and Applied Logic, vol. 84 , pp. 219–255. [REVIEW]Itay Neeman - 2003 - Bulletin of Symbolic Logic 9 (3):414-416.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  20. Saharon Shelah and Hugh Woodin. Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable. Israel journal of mathematics, vol. 70 , pp. 381–394. [REVIEW]Joan Bagaria - 2002 - Bulletin of Symbolic Logic 8 (4):543-545.
  21. W. Hugh Woodin. The axiom of determinacy, forcing axioms, and the nonstationary ideal. De Gruyter series in logic and its applications, no. 1. Walter de Gruyter, Berlin and New York 1999, vi + 934 pp. [REVIEW]Paul B. Larson - 2002 - Bulletin of Symbolic Logic 8 (1):91-93.
  22. Paul Howard and Jean E. Rubin. Consequences of the axiom of choice, Mathematical Surveys and Monographs, vol. 59. American Mathematical Society, Providence, RI, 1998, viii + 432 pp. [REVIEW]Andreas Blass - 2005 - Bulletin of Symbolic Logic 11 (1):61-63.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  23. Constructive Set Theory with Operations.Andrea Cantini & Laura Crosilla - 2007 - In Alessandro Andretta, Keith Kearnes & Domenico Zambella (eds.), Logic Colloquium 2004: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Torino, Italy, July 25-31, 2004. Cambridge: Cambridge University Press.
    We present an extension of constructive Zermelo{Fraenkel set theory [2]. Constructive sets are endowed with an applicative structure, which allows us to express several set theoretic constructs uniformly and explicitly. From the proof theoretic point of view, the addition is shown to be conservative. In particular, we single out a theory of constructive sets with operations which has the same strength as Peano arithmetic.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  24. Hyperintensional Ω-Logic.David Elohim - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer Verlag. pp. 65-82.
    This paper examines the philosophical significance of the consequence relation defined in the $\Omega$-logic for set-theoretic languages. I argue that, as with second-order logic, the hyperintensional profile of validity in $\Omega$-Logic enables the property to be epistemically tractable. Because of the duality between coalgebras and algebras, Boolean-valued models of set theory can be interpreted as coalgebras. In Section \textbf{2}, I demonstrate how the hyperintensional profile of $\Omega$-logical validity can be countenanced within a coalgebraic logic. Finally, in Section \textbf{3}, the philosophical (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  25. No decreasing sequence of cardinals.Paul Howard & Eleftherios Tachtsis - 2016 - Archive for Mathematical Logic 55 (3-4):415-429.
    In set theory without the Axiom of Choice, we investigate the set-theoretic strength of the principle NDS which states that there is no function f on the set ω of natural numbers such that for everyn ∈ ω, f ≺ f, where for sets x and y, x ≺ y means that there is a one-to-one map g : x → y, but no one-to-one map h : y → x. It is a long standing open problem whether NDS implies (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  26. Modal set theory.Christopher Menzel - 2018 - In Otávio Bueno & Scott A. Shalkowski (eds.), The Routledge Handbook of Modality. New York: Routledge.
    This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  27. Characterizing large cardinals in terms of layered posets.Sean Cox & Philipp Lücke - 2017 - Annals of Pure and Applied Logic 168 (5):1112-1131.
  28. On the Theory of Axiom-Systems.Olaf Helmer - 1935 - Analysis 3 (1-2):1-11.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  29. Epistemology of Logic - Logic-Dialectic or Theory of the Knowledge.Epameinondas Xenopoulos - 1998 - Kefalonia,GREECE: KATERINA XENOPOULOU.
    1994.Επιστημολογία της Λογικής. Συγγραφέας Επαμεινώνδας Ξενόπουλος Μοναδική μελέτη και προσέγγιση της θεωρίας της γνώσης, για την παγκόσμια βιβλιογραφία, της διαλεκτικής πορείας της σκέψης από την λογική πλευρά της και της μελλοντικής μορφής που θα πάρουν οι διαλεκτικές δομές της, στην αδιαίρετη ενότητα γνωσιοθεωρίας, λογικής και διαλεκτικής, με την «μέθοδο του διαλεκτικού υλισμού». Έργο βαρύ με θέμα εξαιρετικά δύσκολο διακατέχεται από πρωτοτυπία και ζωντάνια που γοητεύει τον κάθε ανήσυχο στοχαστή από τις πρώτες γραμμές.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  30. Games, scales, and Suslin cardinals. The Cabal Seminar, Volume I, Lecture Notes in Logic, vol. 31.Alessandro Andretta - 2012 - Bulletin of Symbolic Logic 18 (1):122-126.
  31. AD[syntactic turnstile] the [aleph]"n" are Jonsson cardinals and [aleph] omega is a Rowbottom cardinal.E. M. Kleinberg - 1977 - Annals of Mathematical Logic 12 (3):229.
  32. The Necessary Maximality Principle for c. c. c. forcing is equiconsistent with a weakly compact cardinal.Joel D. Hamkins & W. Hugh Woodin - 2005 - Mathematical Logic Quarterly 51 (5):493-498.
    The Necessary Maximality Principle for c. c. c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  33. Some Results on Partitions and Cartesian Products in the Absence of the Axiom of Choice.A. H. Kruse - 1974 - Mathematical Logic Quarterly 20 (8-12):149-172.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  34. Concerning the proper axioms of S4.02.Bolesław Sobociński - 1974 - Notre Dame Journal of Formal Logic 15:169.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  35. Review: The Law of Non-Contradiction: New Philosophical Essays. [REVIEW]Stephen Read - 2007 - Mind 116 (461):203-206.
  36. The cardinals below |[ω1]<ω1|.W. Hugh Woodin - 2006 - Annals of Pure and Applied Logic 140 (1-3):161-232.
    The results of this paper concern the effective cardinal structure of the subsets of [ω1]<ω1, the set of all countable subsets of ω1. The main results include dichotomy theorems and theorems which show that the effective cardinal structure is complicated.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  37. Boolean extensions and measurable cardinals.K. Kunen - 1971 - Annals of Mathematical Logic 2 (4):359.
  38. Powers of regular cardinals.William B. Easton - 1970 - Annals of Mathematical Logic 1 (2):139.
  39. Successive large cardinals.Everett L. Bull - 1978 - Annals of Mathematical Logic 15 (2):161.
  40. omega ¹-Constructible universe and measurable cardinals.Claude Sureson - 1986 - Annals of Pure and Applied Logic 30 (3):293.
  41. Strong compactness and other cardinal sins.Jussi Ketonen - 1972 - Annals of Mathematical Logic 5 (1):47.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  42. Some weak versions of large cardinal axioms.Keith J. Devlin - 1973 - Annals of Mathematical Logic 5 (4):291.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  43. Some combinatorial problems concerning uncountable cardinals.Thomas J. Jech - 1973 - Annals of Mathematical Logic 5 (3):165.
  44. Adding closed cofinal sequences to large cardinals.Lon Berk Radin - 1982 - Annals of Mathematical Logic 22 (3):243.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   24 citations  
  45. Flipping properties: A unifying thread in the theory of large cardinals.F. G. Abramson, L. A. Harrington, E. M. Kleinberg & W. S. Zwicker - 1977 - Annals of Mathematical Logic 12 (1):25.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  46. How many normal measures can ℵmath image carry?Arthur W. Apter - 2010 - Mathematical Logic Quarterly 56 (2):164-170.
    Relative to the existence of a supercompact cardinal with a measurable cardinal above it, we show that it is consistent for ℵ1 to be regular and for ℵmath image to be measurable and to carry precisely τ normal measures, where τ ≥ ℵmath image is any regular cardinal. This extends the work of [2], in which the analogous result was obtained for ℵω +1 using the same hypotheses.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  47. Arrow's Theorem, Weglorz' Models and the Axiom of Choice.Norbert Brunner & H. Reiju Mihara - 2000 - Mathematical Logic Quarterly 46 (3):335-359.
    Applying Weglorz' mode s of set theory without the axiom of choice, we investigate Arrow-type social we fare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying “finite discrimination”, if and only if in Weglorz' mode there is a free ultrafilter on a set representing the individuals.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  48. Sequential topological conditions in ℝ in the absence of the axiom of choice.Gonçalo Gutierres - 2003 - Mathematical Logic Quarterly 49 (3):293-298.
    It is known that – assuming the axiom of choice – for subsets A of ℝ the following hold: (a) A is compact iff it is sequentially compact, (b) A is complete iff it is closed in ℝ, (c) ℝ is a sequential space. We will show that these assertions are not provable in the absence of the axiom of choice, and that they are equivalent to each.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  49. On κ-hereditary Sets and Consequences of the Axiom of Choice.Karl-Heinz Diener - 2000 - Mathematical Logic Quarterly 46 (4):563-568.
    We will prove that some so-called union theorems are equivalent in ZF0 to statements about the transitive closure of relations. The special case of “bounded” union theorems dealing with κ-hereditary sets yields equivalents to statements about the transitive closure of κ-narrow relations. The instance κ = ω1 yields an equivalent to Howard-Rubin's Form 172 of every hereditarily countable set x is countable). In particular, the countable union theorem and, a fortiori, the axiom of countable choice imply Form 172.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  50. Compact and Loeb Hausdorff spaces in equation image and the axiom of choice for families of finite sets.Kyriakos Keremedis - 2012 - Mathematical Logic Quarterly 58 (3):130-138.
    Given a set X, equation image denotes the statement: “equation image has a choice set” and equation image denotes the family of all closed subsets of the topological space equation image whose definition depends on a finite subset of X. We study the interrelations between the statements equation image equation image equation image equation image and “equation imagehas a choice set”. We show: equation image iff equation image iff equation image has a choice set iff equation image. equation image iff (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
1 — 50 / 919