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The Transfer Principle holds for definable nonstandard models under Countable Choice

Author

Listed:
  • Herzberg, Frederik

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Łos’s theorem for (bounded) D-ultrapowers, D being the ultrafilter introduced by Kanovei and Shelah [Journal of Symbolic Logic, 69(1):159–164, 2004], can be established within Zermelo–Fraenkel set theory plus Countable Choice ($ZF+AC_\omega$). Thus, the Transfer Principle for both Kanovei and Shelah’s definable nonstandard model of the reals and Herzberg’s definable nonstandard enlargement of the superstructure over the reals [Mathematical Logic Quarterly, 54(2):167–175; 54(6):666– 667, 2008] can be shown in $ZF+AC_\omega$. This establishes a conjecture by Mikhail Katz [personal communication].

Suggested Citation

  • Herzberg, Frederik, 2016. "The Transfer Principle holds for definable nonstandard models under Countable Choice," Center for Mathematical Economics Working Papers 560, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:560
    as

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    File URL: https://pub.uni-bielefeld.de/download/2904595/2904596
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