Choiceless Löwenheim-Skolem property and uniform definability of grounds

Toshimichi Usuba

Choiceless Löwenheim-Skolem property and uniform definability of grounds

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, without the axiom of choice, we show that if a certain downward Löwenheim-Skolem property holds then all grounds are uniformly definable. We also prove that the axiom of choice is forceable if and only if the universe is a small extension of some transitive model of ZFC.

Original language	English
Journal	Unknown Journal
Publication status	Published - 2019 Apr 1

Keywords

Axiom of Choice
Forcing method
Set-theoretic geology

ASJC Scopus subject areas

General

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