Minimal axiomatic frameworks for definable hyperreals with transfer
classification
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keywords
definableelementaryextensionsuperstructuretransferadditionalassumptionsaxiomatic
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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. Keywords: definability; hyperreal; superstructure; elementary embedding.
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