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 set of all finite subsets of a set
Likewise, for a positive integer
-elements subsets of
For a mapping
, we say that a subset
is free (with respect to
-element subset
Kuratowski published in 1951 the following result, which characterizes the infinite cardinals of the form
ℵ
The theorem states the following.
be a positive integer and let
is greater than or equal to
< ω
-element free subset of
, Kuratowski's free set theorem is superseded by Hajnal's set mapping theorem.
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