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MINIMAL AXIOMATIC FRAMEWORKS FOR DEFINABLE HYPERREALS WITH TRANSFER
Published online by Cambridge University Press: 01 May 2018
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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- Copyright © The Association for Symbolic Logic 2018
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