The Transfer Principle holds for definable nonstandard models under Countable Choice

Frederik Herzberg

No 560, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: Šos’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].

Keywords: nonstandard analysis; Transfer Principle; Axiom of Countable Choice; definability; Šos’s theorem; bounded ultrapower (search for similar items in EconPapers)
Pages: 9
Date: 2016-07-11
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