Minimal Axiomatic Frameworks for Definable Hyperreals with Transfer

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

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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP)
• ISSN: 0022-4812
• Alliance/National Licence: This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
• Language: English