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  1. Constructive Set Theory with Operations.Andrea Cantini & Laura Crosilla - 2008 - In Logic Colloquium 2004.
    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.
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  2. No Decreasing Sequence of Cardinals.Paul Howard & Eleftherios Tachtsis - 2016 - Archive for Mathematical Logic 55 (3-4):415-429.
  3. Modal Set Theory.Christopher Menzel - forthcoming - In Otávio Bueno & Scott Shalkowski (eds.), The Routledge Handbook of Modality. London and New York: Routledge.
    This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.
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  4. Characterizing Large Cardinals in Terms of Layered Posets.Sean Cox & Philipp Lücke - 2017 - Annals of Pure and Applied Logic 168 (5):1112-1131.
  5. Epistemology of Logic - Logic-Dialectic or Theory of the Knowledge.Epameinondas Xenopoulos - 1998 - Dissertation,
    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.
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  6. Axiom of Choice and Complementation.Radu Diaconescu - 1975 - Proceedings of the American Mathematical Society 51 (1):176-178.
    It is shown that an intuitionistic model of set theory with the axiom of choice has to be a classical one.
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  7. Assertion Proof and the Axiom of Choice.David DeVidi - 2006 - In ¸ Itedevidikenyon2006. Springer Verlag.
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  8. The Axiom of Choice Vol. 22.John L. Bell - 2009 - College Publications.
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  9. Pantachies and Weakly Inaccessible Cardinals.Koji Nakatogawa - 1987 - Annals of the Japan Association for Philosophy of Science 7 (2):57-71.
  10. On ^|^Alefsym;0-Complete Cardinals and ^|^Pi;11-Class of Ordinals.Kanji Namba - 1967 - Annals of the Japan Association for Philosophy of Science 3 (2):77-86.
  11. Criteria of Identity and the Axiom of Choice.Timothy Williamson - 1986 - Journal of Philosophy 83 (7):380.
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  12. A Generalized Cut Characterization of the Fullness Axiom in CZF.Laura Crosilla, Erik Palmgren & Peter Schuster - 2013 - Logic Journal of the IGPL 21 (1):63-76.
    In the present note, we study a generalization of Dedekind cuts in the context of constructive Zermelo–Fraenkel set theory CZF. For this purpose, we single out an equivalent of CZF's axiom of fullness and show that it is sufficient to derive that the Dedekind cuts in this generalized sense form a set. We also discuss the instance of this equivalent of fullness that is tantamount to the assertion that the class of Dedekind cuts in the rational numbers, in the customary (...)
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  13. On the Splitting Number at Regular Cardinals.Omer Ben-Neria & Moti Gitik - 2015 - Journal of Symbolic Logic 80 (4):1348-1360.
  14. Axiom I 0 and Higher Degree Theory.Xianghui Shi - 2015 - Journal of Symbolic Logic 80 (3):970-1021.
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  15. Large Cardinals and Lightface Definable Well-Orders, Without the Gch.Sy-David Friedman, Peter Holy & Philipp Lücke - 2015 - Journal of Symbolic Logic 80 (1):251-284.
  16. Determinacy and Jónsson Cardinals in L.S. Jackson, R. Ketchersid, F. Schlutzenberg & W. H. Woodin - 2014 - Journal of Symbolic Logic 79 (4):1184-1198.
  17. Tameness From Large Cardinal Axioms.Will Boney - 2014 - Journal of Symbolic Logic 79 (4):1092-1119.
  18. On ${\Omega _1}$-Strongly Compact Cardinals.Joan Bagaria & Menachem Magidor - 2014 - Journal of Symbolic Logic 79 (1):266-278.
  19. The Strong Tree Property at Successors of Singular Cardinals.Laura Fontanella - 2014 - Journal of Symbolic Logic 79 (1):193-207.
  20. Sampei Yoemon. Note on the Effective Choice of a Point in the Complement of an Analytic Set. Commentarii Mathematici Universitatis Sancti Pauli, Vol. 7 , Pp. 91–95. [REVIEW]M. R. Krom - 1970 - Journal of Symbolic Logic 35 (1):146.
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  21. Quiné W. V.. On the Axiom of Reducibility. Mind, N.S., Vol. 45 , Pp. 498–500.C. H. Langford - 1937 - Journal of Symbolic Logic 2 (1):60.
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  22. Royce Josiah. Axiom. Royce's Logical Essays, Wm. C. Brown Company, Dubuque 1951, Pp. 125–138.Hugues Leblanc - 1952 - Journal of Symbolic Logic 17 (2):143.
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  23. Rubin Herman and Rubin Jean E.. 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.
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  24. Rainbow Ramsey Theorem for Triples is Strictly Weaker Than the Arithmetical Comprehension Axiom.Wei Wang - 2013 - Journal of Symbolic Logic 78 (3):824-836.
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  25. Ramsey-Like Cardinals II.Victoria Gitman & P. D. Welch - 2011 - Journal of Symbolic Logic 76 (2):541-560.
  26. The Independence Of.Amir Leshem & Menachem Magidor - 1999 - Journal of Symbolic Logic 64 (1):350-362.
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  27. Kanamori Akihiro. The Higher Infinite. Large Cardinals in Set Theory From Their Beginnings. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, Heidelberg, New York, Etc., 1994, Xxiv + 536 Pp. [REVIEW]Azriel Levy - 1996 - Journal of Symbolic Logic 61 (1):334-336.
  28. Van Lambalgen Michiel. Independence, Randomness and the Axiom of Choice.John C. Simms - 1994 - Journal of Symbolic Logic 59 (4):1433-1434.
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  29. Moti Gitik. Regular Cardinals in Models of ZF. Transactions of the American Mathematical Society, Vol. 290 , Pp. 41–68.Thomas Jech - 1994 - Journal of Symbolic Logic 59 (2):668.
  30. Larger Cardinals in Cichon's Diagram.Jorg Brendle - 1991 - Journal of Symbolic Logic 56 (3):795.
    We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichon's diagram are equal to $\kappa$ while the others are equal to $\lambda$, where $\kappa < \lambda$ are both arbitrary regular uncountable cardinals. We extend some of these results to the case when $\lambda$ is singular. We also show that $\mathrm{cf}) < \kappa_A$ is consistent with ZFC.
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  31. Moore Gregory H.. Zermelo's Axiom of Choice. Its Origins, Development, and Influence. Studies in the History of Mathematics and Physical Sciences, Vol. 8. Springer-Verlag, New York, Heidelberg, and Berlin, 1982, Xiv + 410 Pp. [REVIEW]Jean E. Rubin - 1984 - Journal of Symbolic Logic 49 (2):659-660.
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  32. Kleinberg E. M.. Strong Partition Properties for Infinite Cardinals.James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (3):463.
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  33. Lévy A.. The Interdependence of Certain Consequences of the Axiom of Choice. Fundamenta Mathematicae, Vol. 54 No. 2 , Pp. 135–157. [REVIEW]David Pincus - 1975 - Journal of Symbolic Logic 40 (3):461.
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  34. Silver Jack H.. 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.
  35. Halpern J. D. And Läuchli H.. A Partition Theorem. Transactions of the American Mathematical Society, Vol. 124 , Pp. 360–367.Halpern J. D. And Lévy A.. The Boolean Prime Ideal Theorem Does Not Imply the Axiom of Choice. Axiomatic Set Theory, Proceedings of Symposia in Pure Mathematics, Vol. 13 Part 1, American Mathematical Society, Providence, Rhode Island, 1971, Pp. 83–134. [REVIEW]David Pincus - 1974 - Journal of Symbolic Logic 39 (1):181-182.
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  36. Singh Shaligram. 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.
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  37. Addison J. W. And Moschovakis Yiannis N.. Some Consequences of the Axiom of Definable Determinateness. Proceedings of the National Academy of Sciences, Vol. 59 , Pp. 708–712.Martin Donald A.. 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.
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  38. Wiśniewski K.. Weakened Forms of the Axiom of Choice for Finite Sets. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 16 , Pp. 615–620. [REVIEW]Azriel Lévy - 1971 - Journal of Symbolic Logic 36 (3):543.
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  39. Mycielski Jan and Steinhaus H.. A Mathematical Axiom Contradicting the Axiom of Choice. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 10 , Pp. 1–3.Mycielski Jan. On the Axiom of Determinateness. Fundamenta Mathematicae, Vol. 53 , Pp. 205–224.Mycielski Jan and Świerczkowski S.. On the Lebesgue Measurability and the Axiom of Determinateness. Fundamenta Mathematicae, Vol. 54 , Pp. 67–71.Mycielski Jan. On the Axiom of Determinateness . Fundamenta Mathematicae, Vol. 59 , Pp. 203–212. [REVIEW]James E. Baumgartner - 1971 - Journal of Symbolic Logic 36 (1):164-166.
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  40. Chang C. C.. 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.
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  41. Kreisel G.. The Axiom of Choice and the Class of Hyperarithmetic Functions. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, Series A, Vol. 65 , Pp. 307–319; Also Indagationes Mathematicae, Vol. 24 , Pp. 307–319. [REVIEW]Yiannis N. Moschovakis - 1970 - Journal of Symbolic Logic 35 (2):333-334.
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  42. Lévy A. And Solovay R. M.. Measurable Cardinals and the Continuum Hypothesis. Israel Journal of Mathematics, Vol. 5 , Pp. 234–248. [REVIEW]F. R. Drake - 1969 - Journal of Symbolic Logic 34 (4):654-655.
  43. Orey Steven. New Foundations and the Axiom of Counting. Duke Mathematical Journal, Vol. 31 , Pp. 655–660.Norman Feldman - 1969 - Journal of Symbolic Logic 34 (4):649.
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  44. Ono Katuzi. On a Practical Way of Describing Formal Deductions. Nagoya Mathematical Journal, Vol. 21 , Pp. 115–121.Ono Katuzi. New Formulation of the Axiom of Choice by Making Use of the Comprehension Operator. Nagoya Mathematical Journal, Vol. 23 , Pp. 53–71. [REVIEW]Elliott Mendelson - 1969 - Journal of Symbolic Logic 34 (2):307.
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  45. Sugihara Takeo. The Numbers of Modalities in T Supplemented by the Axiom CL2pL3p.Krister Segerberg - 1969 - Journal of Symbolic Logic 34 (2):305.
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  46. Bukowský L. And Příkry K.. Some Matamathematical Properties of Measurable Cardinals. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 14 , Pp. 9–14. [REVIEW]Peter G. Hinman - 1968 - Journal of Symbolic Logic 33 (3):476.
  47. Uesu Tadahiro. On Zermelo's Set-Theory and the Simple Type-Theory with the Axiom of Infinity. Commentarti Mathematici Universitatis Sancti Pauli, Vol. 15 , Pp. 49–59. [REVIEW]Bede Rundle - 1968 - Journal of Symbolic Logic 33 (2):292-293.
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  48. Keisler H. J. And Tarski A.. 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.
  49. Scott Dana. Measurable Cardinals and Constructible Sets. Bulletin de l' Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 9 , Pp. 521–524. [REVIEW]Azriel Lévy - 1967 - Journal of Symbolic Logic 32 (3):410.
  50. Halpern J. D.. The Independence of the Axiom of Choice From the Boolean Prime Ideal Theorem. Fundamenta Mathematicae, Vol. 55 , Pp. 57–66. [REVIEW]Elliott Mendelson - 1967 - Journal of Symbolic Logic 32 (2):273-274.
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