Collapsing algebra

In mathematics, a collapsing algebra is a type of Boolean algebra sometimes used in forcing to reduce ("collapse") the size of cardinals. The posets used to generate collapsing algebras were introduced by Azriel Lévy in 1963.

The collapsing algebra of λ^ω is a complete Boolean algebra with at least λ elements but generated by a countable number of elements. As the size of countably generated complete Boolean algebras is unbounded, this shows that there is no free complete Boolean algebra on a countable number of elements.

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