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.

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相关选择的几何条件

我们提供了一个几何条件，该条件表征了 Fraenkel-Mostowski-Specker 排列模型中依赖选择原理何时成立。该条件是要求组过滤器在可数交叉点下关闭的稍微弱化。我们证明这个条件在我们称为“无处密集模型”的新排列模型中并不平凡，并且我们还研究了它对不可数基数的扩展。