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Minimal axiomatic frameworks for definable hyperreals with transfer. (English) Zbl 1447.03014
Summary: We modify the definable ultrapower construction of V. Kanovei and S. Shelah [J. Symb. Log. 69, No. 1, 159–164 (2004; Zbl 1070.03044)] to develop a ZF-definable extension of the continuum with transfer provable using countable choice only, with an additional mild hypothesis on well-ordering implying properness. Under the same assumptions, we also prove the existence of a definable, proper elementary extension of the standard superstructure over the reals.

MSC:
03E35 Consistency and independence results
03C20 Ultraproducts and related constructions
03H05 Nonstandard models in mathematics
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