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arXiv · 1904.00895

Choiceless L\"owenheim-Skolem property and uniform definability of grounds

Toshimichi Usuba
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Abstract

In this paper, without the axiom of choice, we show that if a certain downward L\"owenheim-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 $\mathsf{ZFC}$.

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Toshimichi Usuba. 2019-04-01. Choiceless L\"owenheim-Skolem property and uniform definability of grounds. https://arxiv.org/abs/1904.00895

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