Stationary set

In mathematical set theory and model theory, a stationary set is one that is not too small in the sense that it intersects all club sets, and is analogous to a set of non-zero measure in set theory. There are at least three closely related notions of stationary set, depending on whether one is looking at subsets of an ordinal, or subsets of something of given cardinality, or a powerset.

If ${\displaystyle \kappa \,}$ is a cardinal of uncountable cofinality, ${\displaystyle S\subseteq \kappa \,,}$ and ${\displaystyle S\,}$ intersects every club set in ${\displaystyle \kappa \,,}$ then ${\displaystyle S\,}$ is called a stationary set. If a set is not stationary, then it is called a thin set. This notion should not be confused with the notion of a thin set in number theory.

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