Cofiniteness - Boolean Algebras

Boolean Algebras

The set of all subsets of X that are either finite or cofinite forms a Boolean algebra, i.e., it is closed under the operations of union, intersection, and complementation. This Boolean algebra is the finite-cofinite algebra on X. A Boolean algebra A has a unique non-principal ultrafilter (i.e. a maximal filter not generated by a single element of the algebra) if and only if there is an infinite set X such that A is isomorphic to the finite-cofinite algebra on X. In this case, the non-principal ultrafilter is the set of all cofinite sets.

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Boolean Algebras Canonically Defined
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