Category:Tukey's Lemma

This category contains pages concerning Tukey's Lemma:

Formulation 1

Let $S$ be a non-empty set of finite character.

Then $S$ has an element which is maximal with respect to the subset relation.

Formulation 2

Let $S$ be a non-empty set of finite character.

Then every element of $S$ is a subset of a maximal element of $S$ under the subset relation.