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  1. W. Ackermann (1950). Tarski Alfred. Axiomatic and Algebraic Aspects of Two Theorems on Sums of Cardinals. Ebd., S. 79–104. Journal of Symbolic Logic 14 (4):257-258.
  2. Arthur W. Apter (2016). Indestructibility and Destructible Measurable Cardinals. Archive for Mathematical Logic 55 (1-2):3-18.
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  3. Arthur W. Apter (2009). Indestructibility and Stationary Reflection. Mathematical Logic Quarterly 55 (3):228-236.
    If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ -strategically closed forcing and λ is weakly compact, then we show thatA = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets}must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to construct a model where no cardinal is supercompact up to a (...)
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  4. Arthur W. Apter (2009). Indestructibility Under Adding Cohen Subsets and Level by Level Equivalence. Mathematical Logic Quarterly 55 (3):271-279.
    We construct a model for the level by level equivalence between strong compactness and supercompactness in which the least supercompact cardinal κ has its strong compactness indestructible under adding arbitrarily many Cohen subsets. There are no restrictions on the large cardinal structure of our model.
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  5. Joan Bagaria (2002). Israel Journal of Mathematics. 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] Bulletin of Symbolic Logic 8 (4):543-545.
  6. Joan Bagaria, Joel David Hamkins, Konstantinos Tsaprounis & Toshimichi Usuba (2016). Superstrong and Other Large Cardinals Are Never Laver Indestructible. Archive for Mathematical Logic 55 (1-2):19-35.
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  7. Joan Bagaria & Menachem Magidor (2014). On ${\Omega _1}$-Strongly Compact Cardinals. Journal of Symbolic Logic 79 (1):266-278.
  8. Frederick Bagemihl (1959). Some Results Connected with the Continuum Hypothesis. Mathematical Logic Quarterly 5 (7‐13):97-116.
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  9. Frederick Bagemihl (1959). Some Results Connected with the Continuum Hypothesis. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5 (7-13):97-116.
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  10. J. L. Bell (1974). On Compact Cardinals. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (25-27):389-393.
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  11. Omer Ben-Neria & Moti Gitik (2015). On the Splitting Number at Regular Cardinals. Journal of Symbolic Logic 80 (4):1348-1360.
  12. Paul Bernays (1940). Gödel Kurt. Consistency-Proof for the Generalized Continuum-Hypothesis. Proceedings of the National Academy of Sciences, Vol. 25 , Pp. 220–224. [REVIEW] Journal of Symbolic Logic 5 (3):117-118.
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  13. M. Boffa (1973). 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] Journal of Symbolic Logic 38 (4):652.
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  14. Jorg Brendle (1991). Larger Cardinals in Cichon's Diagram. Journal of Symbolic Logic 56 (3):795.
  15. Everett L. Bull (1978). Successive Large Cardinals. Annals of Mathematical Logic 15 (2):161-191.
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  16. Yong Cheng, Sy-David Friedman & Joel David Hamkins (2015). Large Cardinals Need Not Be Large in HOD. Annals of Pure and Applied Logic 166 (11):1186-1198.
  17. Yong Cheng & Victoria Gitman (2015). Indestructibility Properties of Remarkable Cardinals. Archive for Mathematical Logic 54 (7-8):961-984.
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  18. Paul E. Cohen (1974). L-Mahlo Cardinals. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (13-18):229-231.
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  19. Paul Corazza (2010). The Axiom of Infinity and Transformations J: V→V. 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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  20. James W. Cummings (2000). Apter Arthur W.. On the Least Strongly Compact Cardinal. Israel Journal of Mathematics, Vol. 35 , Pp. 225–233.Apter Arthur W.. Measurability and Degrees of Strong Compactness. The Journal of Symbolic Logic, Vol. 46 , Pp. 249–254.Apter Arthur W.. A Note on Strong Compactness and Supercompactness. Bulletin of the London Mathematical Society, Vol. 23 , Pp. 113–115.Apter Arthur W.. On the First N Strongly Compact Cardinals. Proceedings of the American Mathematical Society, Vol. 123 , Pp. 2229–2235.Apter Arthur W. And Shelah Saharon. On the Strong Equality Between Supercompactness and Strong Compactness.. Transactions of the American Mathematical Society, Vol. 349 , Pp. 103–128.Apter Arthur W. And Shelah Saharon. Menas' Result is Best Possible. Ibid., Pp. 2007–2034.Apter Arthur W.. More on the Least Strongly Compact Cardinal. Mathematical Logic Quarterly, Vol. 43 , Pp. 427–430.Apter Arthur W.. Laver Indestructibility and the Class of Compact Cardinals. The Journal of Symbolic Logic, Vol. 63. [REVIEW] Bulletin of Symbolic Logic 6 (1):86-89.
  21. James Cummings, Sy David Friedman & Mohammad Golshani (2015). Collapsing the Cardinals of HOD. Journal of Mathematical Logic 15 (2):1550007.
  22. Keith J. Devlin (1980). Concerning the Consistency of the Souslin Hypothesis with the Continuum Hypothesis. Annals of Mathematical Logic 19 (1-2):115-125.
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  23. F. R. Drake (1973). Rieger L.. On the Consistency of the Generalized Continuum Hypothesis. Rozprawy Matematyczne No. 31. Państwowe Wydawnictwo Naukowe, Warsaw 1963, 45 Pp. [REVIEW] Journal of Symbolic Logic 38 (1):153.
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  24. F. R. Drake (1973). Review: L. Rieger, On the Consistency of the Generalized Continuum Hypothesis. [REVIEW] Journal of Symbolic Logic 38 (1):153-153.
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  25. F. R. Drake (1969). Lévy A. And Solovay R. M.. Measurable Cardinals and the Continuum Hypothesis. Israel Journal of Mathematics, Vol. 5 , Pp. 234–248. [REVIEW] Journal of Symbolic Logic 34 (4):654-655.
  26. William B. Easton (1965). Cohen Paul J.. The Independence of the Continuum Hypothesis. Proceedings of the National Academy of Sciences of the United States of America, Vol. 50 , Pp. 1143–1148, and Vol. 51 , Pp. 105–110. [REVIEW] Journal of Symbolic Logic 30 (3):398-403.
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  27. Laura Fontanella (2014). The Strong Tree Property at Successors of Singular Cardinals. Journal of Symbolic Logic 79 (1):193-207.
  28. Sy D. Friedman (2005). Definability Degrees. Mathematical Logic Quarterly 51 (5):448-449.
    We establish the equiconsistency of a simple statement in definability theory with the failure of the GCH at all infinite cardinals. The latter was shown by Foreman and Woodin to be consistent, relative to the existence of large cardinals.
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  29. Sy D. Friedman (2005). Genericity and Large Cardinals. Journal of Mathematical Logic 5 (02):149-166.
  30. Sy D. Friedman (2003). Cardinal-Preserving Extensions. Journal of Symbolic Logic 68 (4):1163-1170.
    A classic result of Baumgartner-Harrington-Kleinberg [1] implies that assuming CH a stationary subset of ω1 has a CUB subset in a cardinal-perserving generic extension of V, via a forcing of cardinality ω1. Therefore, assuming that $\omega_2^L$ is countable: { $X \in L \mid X \subseteq \omega_1^L$ and X has a CUB subset in a cardinal -preserving extension of L} is constructible, as it equals the set of constructible subsets of $\omega_1^L$ which in L are stationary. Is there a similar such (...)
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  31. Sy-David Friedman, Peter Holy & Philipp Lücke (2015). Large Cardinals and Lightface Definable Well-Orders, Without the Gch. Journal of Symbolic Logic 80 (1):251-284.
  32. Sy-David Friedman, Radek Honzik & Lyubomyr Zdomskyy (2013). Fusion and Large Cardinal Preservation. Annals of Pure and Applied Logic 164 (12):1247-1273.
  33. Sy-David Friedman & Philipp Lücke (2015). Large Cardinals and Definable Well-Orders, Without the GCH. Annals of Pure and Applied Logic 166 (3):306-324.
  34. W. Gielen, H. De Swart & W. Veldman (1981). The Continuum Hypothesis in Intuitionism. Journal of Symbolic Logic 46 (1):121 - 136.
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  35. Victoria Gitman & P. D. Welch (2011). Ramsey-Like Cardinals II. Journal of Symbolic Logic 76 (2):541-560.
  36. John Gregory (1976). Higher Souslin Trees and the Generalized Continuum Hypothesis. Journal of Symbolic Logic 41 (3):663-671.
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  37. Walter Gumbley (1938). Cardinals of English Sees. New Blackfriars 19 (215):83-91.
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  38. P. K. H. (1967). Set Theory and the Continuum Hypothesis. [REVIEW] Review of Metaphysics 20 (4):716-716.
  39. Stephen H. Hechler (1973). Powers of Singular Cardinals and a Strong Form of The Negation of The Generalized Continuum Hypothesis. Mathematical Logic Quarterly 19 (3‐6):83-84.
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  40. Stephen H. Hechler (1973). Powers of Singular Cardinals and a Strong Form of The Negation of The Generalized Continuum Hypothesis. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 19 (3-6):83-84.
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  41. Michał Heller & W. H. Woodin (eds.) (2011). Infinity: New Research Frontiers. Cambridge University Press.
    Machine generated contents note: Introduction Rudy Rucker; Part I. Perspectives on Infinity from History: 1. Infinity as a transformative concept in science and theology Wolfgang Achtner; Part II. Perspectives on Infinity from Mathematics: 2. The mathematical infinity Enrico Bombieri; 3. Warning signs of a possible collapse of contemporary mathematics Edward Nelson; Part III. Technical Perspectives on Infinity from Advanced Mathematics: 4. The realm of the infinite W. Hugh Woodin; 5. A potential subtlety concerning the distinction between determinism and nondeterminism W. (...)
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  42. J. M. Henle & E. M. Kleinberg (1978). A Flipping Characterization of Ramsey Cardinals. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (1-6):31-36.
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  43. John L. Hickman (1979). Boundedness Properties of Cardinals. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (31):485-486.
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  44. Peter G. Hinman (1968). 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] Journal of Symbolic Logic 33 (3):476.
  45. Paul Howard & Eleftherios Tachtsis (forthcoming). No Decreasing Sequence of Cardinals. Archive for Mathematical Logic.
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  46. S. Jackson, R. Ketchersid, F. Schlutzenberg & W. H. Woodin (2014). Determinacy and Jónsson Cardinals in L. Journal of Symbolic Logic 79 (4):1184-1198.
  47. I. Jane (2010). Idealist and Realist Elements in Cantor's Approach to Set Theory. Philosophia Mathematica 18 (2):193-226.
    There is an apparent tension between the open-ended aspect of the ordinal sequence and the assumption that the set-theoretical universe is fully determinate. This tension is already present in Cantor, who stressed the incompletable character of the transfinite number sequence in Grundlagen and avowed the definiteness of the totality of sets and numbers in subsequent philosophical publications and in correspondence. The tension is particularly discernible in his late distinction between sets and inconsistent multiplicities. I discuss Cantor’s contrasting views, and I (...)
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  48. Thomas Jech (1994). Moti Gitik. Regular Cardinals in Models of ZF. Transactions of the American Mathematical Society, Vol. 290 , Pp. 41–68. Journal of Symbolic Logic 59 (2):668.
  49. C. A. Johnson (1986). Precipitous Ideals on Singular Cardinals. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (25-30):461-465.
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  50. Akihiro Kanamori (1994). The Higher Infinite Large Cardinals in Set Theory From Their Beginnings.
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