The Transfer Principle holds for definable nonstandard models under Countable Choice

Herzberg F (2016) Center for Mathematical Economics Working Papers; 560.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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].
Stichworte
nonstandard analysis; Transfer Principle; Axiom of Countable Choice; definability; Łos’s theorem; bounded ultrapower
Erscheinungsjahr
2016
Band
560
Seite(n)
9
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2904595

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Herzberg F. The Transfer Principle holds for definable nonstandard models under Countable Choice. Center for Mathematical Economics Working Papers. Vol 560. Bielefeld: Center for Mathematical Economics; 2016.
Herzberg, F. (2016). The Transfer Principle holds for definable nonstandard models under Countable Choice (Center for Mathematical Economics Working Papers, 560). Bielefeld: Center for Mathematical Economics.
Herzberg, F. (2016). The Transfer Principle holds for definable nonstandard models under Countable Choice. Center for Mathematical Economics Working Papers, 560, Bielefeld: Center for Mathematical Economics.
Herzberg, F., 2016. The Transfer Principle holds for definable nonstandard models under Countable Choice, Center for Mathematical Economics Working Papers, no.560, Bielefeld: Center for Mathematical Economics.
F. Herzberg, The Transfer Principle holds for definable nonstandard models under Countable Choice, Center for Mathematical Economics Working Papers, vol. 560, Bielefeld: Center for Mathematical Economics, 2016.
Herzberg, F.: The Transfer Principle holds for definable nonstandard models under Countable Choice. Center for Mathematical Economics Working Papers, 560. Center for Mathematical Economics, Bielefeld (2016).
Herzberg, Frederik. The Transfer Principle holds for definable nonstandard models under Countable Choice. Bielefeld: Center for Mathematical Economics, 2016. Center for Mathematical Economics Working Papers. 560.
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2019-09-06T09:18:38Z
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