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Nonregular ultrafilters and large cardinals


Author: Jussi Ketonen
Journal: Trans. Amer. Math. Soc. 224 (1976), 61-73
MSC: Primary 02K30; Secondary 04A20
DOI: https://doi.org/10.1090/S0002-9947-1976-0419236-X
MathSciNet review: 0419236
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Abstract: The relationship between the existence of nonregular ultrafilters and large cardinals in the constructible universe is studied.


References [Enhancements On Off] (What's this?)

  • [1] M. Benda and J. Ketonen, On regularity of ultrafilters, Israel J. Math. 17 (1974), 231-240. MR 0396264 (53:132)
  • [2] C. C. Chang and H. J. Keisler, Model theory, North Holland, Amsterdam, 1973.
  • [3] R. Jensen, Some combinatorial principles of L (Mimeographed).
  • [4] K. Devlin, Some weak versions of large cardinality axioms, Ann. Math. Logic 5 (1973), 291-326. MR 0363906 (51:161)
  • [5] A. Kanamori, Ultrafilters over uncountable cardinals, Doctoral Dissertation, Univ. of Cambridge, 1975.
  • [6] H. J. Keisler, Limit ultrapowers, Trans. Amer. Math. Soc. 107 (1963), 382-408. MR 26 #6054. MR 0148547 (26:6054)
  • [7] J. Ketonen, Strong compactness and other cardinal sins, Ann. Math. Logic 5 (1972), 47-76. MR 0469768 (57:9549)
  • [8] -, Open problems in the theory of ultrafilters (to appear).
  • [9] K. Kunen, Inaccessibility properties of cardinals, Doctoral Dissertation, Stanford Univ., 1968.
  • [10] -, Some applications of iterated ultrapowers in set theory, Ann. Math. Logic 1 (1970), 179-227. MR 43 #3080. MR 0277346 (43:3080)
  • [11] -, Ultrafilters and independents sets, Trans. Amer. Math. Soc. 172 (1972), 299-306. MR 47 #3170. MR 0314619 (47:3170)
  • [12] K. Prikry, Changing measurable into accessible cardinals, Dissertationes Math. Rozprawy Mat. 68 (1970), 1-55. MR 41 #6685. MR 0262075 (41:6685)
  • [13] -, On a problem of Gillman and Keisler, Ann. Math. Logic 2 (1970), 179-187. MR 42 #4408. MR 0269513 (42:4408)
  • [14] -, On descendingly complete ultrafilters (to appear).
  • [15] D. S. Scott, Measurable cardinals and constructible sets, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961), 521-524. MR 26 #1263. MR 0143710 (26:1263)
  • [16] J. Silver, Indecomposable ultrafilters and 0$ ^{\char93 }$ (to appear). MR 0360276 (50:12726)
  • [17] R. Solovay and D. Scott, Boolean-valued models for set theory, Proc. 1967 U.C.L.A. Summer Inst. (to appear).
  • [18] R. M. Solovay, A nonconstructible $ \Delta _3^1$ set of integers, Trans. Amer. Math. Soc. 127 (1967), 50-75. MR 35 #2748. MR 0211873 (35:2748)
  • [19] P. Vopěnka, An estimate of cardinality of a power, J. Symbolic Logic 35 (1970), 612. (Abstract).
  • [20] P. Vopěnka and K. Hrbáček, On strongly measurable cardinals, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 14 (1966), 587-591. MR 35 #2747. MR 0211872 (35:2747)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0419236-X
Keywords: Ultrafilter, nonregular, weak compactness, weak normality
Article copyright: © Copyright 1976 American Mathematical Society

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