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MINIMAL AXIOMATIC FRAMEWORKS FOR DEFINABLE HYPERREALS WITH TRANSFER

  • FREDERIK S. HERZBERG (a1), VLADIMIR KANOVEI (a2), MIKHAIL KATZ (a3) and VASSILY LYUBETSKY (a4)
Abstract

We modify the definable ultrapower construction of Kanovei and Shelah (2004) 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.

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  • ISSN: 0022-4812
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