Geometric condition for Dependent Choice
Logic
2024-04-22 v3
Abstract
We provide a geometric condition which characterises when the Principle of Dependent Choice holds in a Fraenkel--Mostowski--Specker permutation model. This condition is a slight weakening of requiring the filter of groups to be closed under countable intersections. We show that this condition holds nontrivially in a new permutation model we call "the nowhere dense model" and we study its extensions to uncountable cardinals as well.
Keywords
Cite
@article{arxiv.2212.10261,
title = {Geometric condition for Dependent Choice},
author = {Asaf Karagila and Jonathan Schilhan},
journal= {arXiv preprint arXiv:2212.10261},
year = {2024}
}
Comments
5 pages+references; final version accepted for publication