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Successive weakly compact or singular cardinals

  • Ralf-Dieter Schindler (a1) (a2) (a3)

It is shown in ZF that if δ < δ+ < Ω are such that δ and δ+ are either both weakly compact or singular cardinals and Ω is large enough for putting the core model apparatus into action then there is an inner model with a Woodin cardinal.

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[3] D. A. Martin and J. R. Steel , A proof of projective determinacy, Journal of the American Mathematical Society, vol. 2 (1989), pp. 71–125.

[5] W. J. Mitchell and E. Schimmerling , Covering without countable closure, Mathematical Research Letters, vol. 2 (1995), pp. 595–609.

[6] W. J. Mitchell , E. Schimmerling , and J. R. Steel , The covering lemma up to a Woodin cardinal, Annals of Pure and Applied Logic, vol. 84 (1997), pp. 219–255.

[7] W. J. Mitchell and J. R. Steel , Fine structure and iteration trees, Lecture Notes in Logic, Springer-Verlag, Berlin, 1994.

[10] R.-D. Schindler , Weak covering at large cardinals, Mathematical Logic Quarterly, vol. 43 (1997), pp. 22–28.

[12] J. R. Steel , HODL(ℝ) is a core model below Θ, The Bulletin of Symbolic Logic, vol. 1 (1995), pp. 75–84.

[13] J. R. Steel , The core model iterability problem, Lecture Notes in Logic, Springer-Verlag, Berlin, 1996.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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