Title: Minimal axiomatic frameworks for definable hyperreals with transfer,
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.
Keywords: definability; hyperreal; superstructure; elementary embedding.