Minimal axiomatic frameworks for definable hyperreals with transfer

Frederik S. Herzberg，Vladimir Kanovei，Mikhail Katz，Vassily Lyubetsky

【摘要】我们修改了Kanovei和Shelah(2004)的可定义的超幂结构，仅用可数选择（公理），再加上一个关于良序的温和假设，即适当，建立了一个ZF-可定义的有变换（transfer）的连续体扩张。在同样的假设下，我们还证明了实数上的标准上层建筑一个可定义的、恰当的初等扩张的存在性。

关键词：可定义性；超实数；上层建筑。

【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.

Matches for: MR=3796290​mathscinet.ams.orgMinimal axiomatic frameworks for definable hyperreals with transfer​arxiv.orghttp://dx.doi.org/10.1017/jsl.2017.48​dx.doi.org