Abstract

We provide a geometric condition which characterises when thePrinciple of Dependent Choice holds in a Fraenkel-Mostowski-Specker permutationmodel. This condition is a slight weakening of requiring the filter of groups tobe closed under countable intersections. We show that this condition holds nontriviallyin a new permutation model we call "the nowhere dense model" and westudy its extensions to uncountable cardinals as well.

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