TY  - GEN
AB  - 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].
DA  - 2016
KW  - nonstandard analysis
KW  - Transfer Principle
KW  - Axiom of Countable Choice
KW  - definability
KW  - Łos’s theorem
KW  - bounded ultrapower
LA  - eng
PY  - 2016
SN  - 0931-6558
SP  - 9-
TI  - The Transfer Principle holds for definable nonstandard models under Countable Choice
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29045953
Y2  - 2024-11-22T07:45:46
ER  -