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Herzberg, Frederik S.; Kanovei, Vladimir; Katz, Mikhail and Lyubetsky, Vassily (2018): Minimal Axiomatic Frameworks for Definable Hyperreals with Transfer. In: Journal of Symbolic Logic, Vol. 83, No. 1: pp. 385-391 [PDF, 122kB]


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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