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 (1963).
Definition
There are several slightly different sorts of collapsing algebras.
If κ and λ are cardinals, then the Boolean algebra of regular open sets of the product space κλ is a collapsing algebra. Here κ and λ are both given the discrete topology. There are several different options for the topology of κλ. The simplest option is to take the usual product topology. Another option is to take the topology generated by open sets consisting of functions whose value is specified on less than λ elements of λ.
References
- Bell, J. L. (1985) Boolean-Valued Models and Independence Proofs in Set Theory, Oxford. ISBN 0-19-853241-5
- Jech, Thomas (2002). Set theory, third millennium edition (revised and expanded). Springer. ISBN 3-540-44085-2. OCLC 174929965.
- Lévy (1963), "Independence results in set theory by Cohen's method. IV", Notices Amer. Math. Soc., 10: 593
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