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  1. 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.
  2. 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.
  3. A. Lévy and R. M. Solovay. 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.
  4. Bolesław Sobociński. A Note on the Generalized Continuum Hypothesis. Notre Dame Journal of Formal Logic, Vol. 3 , Pp. 274–278, and Vol. 4 , Pp. 67–79, 233–240. [REVIEW]Leslie H. Tharp - 1969 - Journal of Symbolic Logic 33 (4):632.
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  5. Bolesław Sobociński. A Note on the Generalized Continuum Hypothesis. Notre Dame Journal of Formal Logic, Vol. 3 , Pp. 274–278, and Vol. 4 , Pp. 67–79, 233–240. [REVIEW]Leslie H. Tharp - 1969 - Journal of Symbolic Logic 33 (4):632.
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  6. Richard A. Platek. Eliminating the Continuum Hypothesis. The Journal of Symbolic Logic, Vol. 34 , Pp. 219–225.E. G. K. Lopez-Escobar - 1971 - Journal of Symbolic Logic 36 (1):166.
  7. Richard A. Platek. Eliminating the Continuum Hypothesis. The Journal of Symbolic Logic, Vol. 34 , Pp. 219–225.E. G. K. Lopez-Escobar - 1971 - Journal of Symbolic Logic 36 (1):166.
  8. Cohen Paul J.. Set Theory and the Continuum Hypothesis. W. A. Benjamin, Inc., New York and Amsterdam 1966, Vi + 154 Pp. [REVIEW]Kenneth Kunen - 1970 - Journal of Symbolic Logic 35 (4):591-592.
  9. Cohen Paul J.. Set Theory and the Continuum Hypothesis. W. A. Benjamin, Inc., New York and Amsterdam 1966, Vi + 154 Pp. [REVIEW]Kenneth Kunen - 1970 - Journal of Symbolic Logic 35 (4):591-592.
  10. Rolf Schock. A Simple Version of the Generalized Continuum Hypothesis. Notre Dame Journal of Formal Logic, Vol. 7 No. 3 , Pp. 287–288. [REVIEW]J. R. Shoenfield - 1970 - Journal of Symbolic Logic 35 (4):592.
  11. Rolf Schock. A Simple Version of the Generalized Continuum Hypothesis. Notre Dame Journal of Formal Logic, Vol. 7 No. 3 , Pp. 287–288. [REVIEW]J. R. Shoenfield - 1970 - Journal of Symbolic Logic 35 (4):592.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. The Axiom of Infinity and Transformations J: V → V.Paul Corazza - 2010 - Bulletin of Symbolic Logic 16 (1):37-84.
    We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals ought to be derivable? (...)
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  17. The Counterparts to Statements That Are Equivalent to the Continuum Hypothesis.Asger Törnquist & William Weiss - 2015 - Journal of Symbolic Logic 80 (4):1075-1090.
  18. The Counterparts to Statements That Are Equivalent to the Continuum Hypothesis.Asger Törnquist & William Weiss - 2015 - Journal of Symbolic Logic 80 (4):1075-1090.
  19. 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 (...)
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  20. Characterizing Large Cardinals in Terms of Layered Posets.Sean Cox & Philipp Lücke - 2017 - Annals of Pure and Applied Logic 168 (5):1112-1131.
  21. Christine Redecker. Wittgensteins Philosophie der Mathematik: Eine Neubewertung Im Ausgang von der Kritik an Cantors Beweis der Überabzählbarkeit der Reellen Zahlen. [Wittgenstein's Philosophy of Mathematics: A Reassessment Starting From the Critique of Cantor's Proof of the Uncountability of the Real Numbers]: Critical Studies/Book Reviews.Esther Ramharter - 2009 - Philosophia Mathematica 17 (3):382-392.
  22. 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.
  23. 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.
  24. 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.
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  25. 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.
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  26. Boolean Extensions and Measurable Cardinals.K. Kunen - 1971 - Annals of Pure and Applied Logic 2 (4):359.
  27. Powers of Regular Cardinals.William B. Easton - 1970 - Annals of Pure and Applied Logic 1 (2):139.
  28. Successive Large Cardinals.Everett L. Bull - 1978 - Annals of Pure and Applied Logic 15 (2):161.
  29. Concerning the Consistency of the Souslin Hypothesis with the Continuum Hypothesis.Keith J. Devlin - 1980 - Annals of Pure and Applied Logic 19 (1):115.
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  30. Omega ¹-Constructible Universe and Measurable Cardinals.Claude Sureson - 1986 - Annals of Pure and Applied Logic 30 (3):293.
  31. Some Combinatorial Problems Concerning Uncountable Cardinals.Thomas J. Jech - 1973 - Annals of Pure and Applied Logic 5 (3):165.
  32. 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.
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  33. The Power-Set Theorem and the Continuum Hypothesis: A Dialogue Concerning Infinite Number.John-Michael Kuczynski - 2016 - Amazon Digital Services LLC.
    The nature of of Infinite Number is discussed in a rigorous but easy-to-follow manner. Special attention is paid to Cantor's proof that any given set has more subsets than members, and it is discussed how this fact bears on the question: How many infinite numbers are there? This work is ideal for people with little or no background in set theory who would like an introduction to the mathematics of the infinite.
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  34. Pantachies and Weakly Inaccessible Cardinals.Koji Nakatogawa - 1987 - Annals of the Japan Association for Philosophy of Science 7 (2):57-71.
  35. 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.
  36. On the Splitting Number at Regular Cardinals.Omer Ben-Neria & Moti Gitik - 2015 - Journal of Symbolic Logic 80 (4):1348-1360.
    Letκ, λ be regular uncountable cardinals such that λ >κ+is not a successor of a singular cardinal of low cofinality. We construct a generic extension withs = λ starting from a ground model in whicho = λ and prove that assuming ¬0¶,s = λ implies thato ≥ λ in the core model.
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  37. 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.
  38. Determinacy and Jónsson Cardinals in L.S. Jackson, R. Ketchersid, F. Schlutzenberg & W. H. Woodin - 2014 - Journal of Symbolic Logic 79 (4):1184-1198.
    Assume ZF + AD +V=L and letκ< Θ be an uncountable cardinal. We show thatκis Jónsson, and that if cof = ω thenκis Rowbottom. We also establish some other partition properties.
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  39. Tameness From Large Cardinal Axioms.Will Boney - 2014 - Journal of Symbolic Logic 79 (4):1092-1119.
    We show that Shelah’s Eventual Categoricity Conjecture for successors follows from the existence of class many strongly compact cardinals. This is the first time the consistency of this conjecture has been proven. We do so by showing that every AEC withLS below a strongly compact cardinalκis <κ-tame and applying the categoricity transfer of Grossberg and VanDieren [11]. These techniques also apply to measurable and weakly compact cardinals and we prove similar tameness results under those hypotheses. We isolate a dual property (...)
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  40. On ${\Omega _1}$-Strongly Compact Cardinals.Joan Bagaria & Menachem Magidor - 2014 - Journal of Symbolic Logic 79 (1):266-278.
  41. The Strong Tree Property at Successors of Singular Cardinals.Laura Fontanella - 2014 - Journal of Symbolic Logic 79 (1):193-207.
  42. Higher Souslin Trees and the Generalized Continuum Hypothesis.John Gregory - 1976 - Journal of Symbolic Logic 41 (3):663-671.
  43. -Definability at Uncountable Regular Cardinals.Philipp Lücke - 2012 - Journal of Symbolic Logic 77 (3):1011-1046.
    Let k be an infinite cardinal. A subset of $(^k k)^n $ is a $\Sigma _1^1 $ -subset if it is the projection p[T] of all cofinal branches through a subtree T of $(lt;kk)^{n + 1} $ of height k. We define $\Sigma _k^1 - ,\Pi _k^1 $ - and $\Delta _k^1$ subsets of $(^k k)^n $ as usual. Given an uncountable regular cardinal k with k = k (...))
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  44. Ramsey-Like Cardinals II.Victoria Gitman & P. D. Welch - 2011 - Journal of Symbolic Logic 76 (2):541-560.
  45. 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.
  46. 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):668-668.
  47. 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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  48. Gregory John. Higher Souslin Trees and the Generalized Continuum Hypothesis.Daniel Velleman - 1984 - Journal of Symbolic Logic 49 (2):663-665.
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  49. Příkrý K.. The Consistency of the Continuum Hypothesis for the First Measurable Cardinal. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 13 , Pp. 193–197. [REVIEW]M. Boffa - 1973 - Journal of Symbolic Logic 38 (4):652-652.
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  50. Rieger L.. On the Consistency of the Generalized Continuum Hypothesis. Rozprawy Matematyczne No. 31. Państwowe Wydawnictwo Naukowe, Warsaw 1963, 45 Pp. [REVIEW]F. R. Drake - 1973 - Journal of Symbolic Logic 38 (1):153-153.
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