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Some Remarks on Tall Cardinals and Failures of GCH

Autorzy
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate two global GCH patterns which are consistent with the existence of a tall cardinal, and also present some related open questions.
Rocznik
Strony
97--106
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Department of Mathematics Baruch College of CUNY New York, NY 10010, U.S.A.
  • The CUNY Graduate Center, Mathematics 365 Fifth Avenue New York, NY 10016, U.S.A.
Bibliografia
  • [1] A. Apter, Indestructibility, measurability, and degrees of supercompactness, Math. Logic Quart. 58 (2012), 75–82.
  • [2] A. Apter, Level by level in equivalence, strong compactness, and GCH, Bull. Polish Acad. Sci. Math. 60 (2012), 201–209.
  • [3] A. Apter, On a problem of Woodin, Arch. Math. Logic 39 (2000), 253–259.
  • [4] A. Apter, On some questions concerning strong compactness, Arch. Math. Logic 51 (2012), 819–829.
  • [5] A. Apter and J. Cummings, Identity crises and strong compactness II: Strong cardinals, Arch. Math. Logic 40 (2001), 25–38.
  • [6] A. Apter and M. Gitik, On tall cardinals and some related generalizations, Israel J. Math., to appear.
  • [7] B. Cody and M. Magidor, On supercompactness and the continuum function, Ann. Pure Appl. Logic 165 (2014), 620–630.
  • [8] M. Foreman and W. H. Woodin, The generalized continuum hypothesis can fail everywhere, Ann. of Math. 133 (1991), 1–35.
  • [9] S.-D. Friedman and M. Golshani, Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH, Fund. Math. 223 (2013), 171–193.
  • [10] S.-D. Friedman and M. Golshani, Killing the GCH everywhere with a single real, J. Symbolic Logic 78 (2013), 803–823.
  • [11] S.-D. Friedman and R. Honzik, Easton’s theorem and large cardinals, Ann. Pure Appl. Logic 154 (2008), 191–208.
  • [12] M. Gitik, personal communication.
  • [13] J. D. Hamkins, Tall cardinals, Math. Logic Quart. 55 (2009), 68–86.
  • [14] J. D. Hamkins, The lottery preparation, Ann. Pure Appl. Logic 101 (2000), 103–146.
  • [15] T. Jech, Set Theory. The Third Millennium Edition, Revised and Expanded, Springer, Berlin, 2003.
  • [16] A. Kanamori, The Higher Infinite, 2nd ed., Springer, Berlin, 2003.
  • [17] A. Lévy and R. Solovay, Measurable cardinals and the Continuum Hypothesis, Israel J. Math. 5 (1967), 234–248.
  • [18] M. Magidor, How large is the first strongly compact cardinal? or A study on identity crises, Ann. Math. Logic 10 (1976), 33–57.
  • [19] T. Menas, Consistency results concerning supercompactness, Trans. Amer. Math. Soc. 223 (1976), 61–91.
  • [20] C. Merimovich, A power function with a fixed finite gap everywhere, J. Symbolic Logic 72 (2007), 361–417.
  • [21] R. Solovay, Strongly compact cardinals and the GCH, in: Proceedings of the Tarski Symposium, Proc. Sympos. Pure Math. 25, Amer. Math. Soc., Providence, RI, 1974, 365–372.
  • [22] M. Zeman, Inner Models and Large Cardinals, de Gruyter Ser. Logic Appl. 5, de Gruyter, Berlin, 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f5fef2eb-f272-4111-8bf8-d35ce81b1467
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