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About: Kuratowski's free set theorem     Goto   Sponge   NotDistinct   Permalink

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Kuratowski's free set theorem, named after Kazimierz Kuratowski, is a result of set theory, an area of mathematics. It is a result which has been largely forgotten for almost 50 years, but has been applied recently in solving several lattice theory problems, such as the congruence lattice problem. The theorem states the following. Let be a positive integer and let be a set. Then the cardinality of is greater than or equal to if and only if for every mapping from to ,there exists an -element free subset of with respect to . For , Kuratowski's free set theorem is superseded by .