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.
|Publication status||Published - 2019 Apr 1|
- Axiom of Choice
- Forcing method
- Set-theoretic geology
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