Complete quotient Boolean algebras

Akihiro Kanamori; Saharon Shelah

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Complete quotient Boolean algebras

Akihiro Kanamori·Saharon Shelah

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Abstract

For I a proper, countably complete ideal on P(X) for some set X, can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal kappa, and that I is a kappa-complete ideal on P(kappa) containing all singletons. In this paper we provide consequences from and consistency results about completeness.

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BibTeX RIS

Akihiro Kanamori, Saharon Shelah. 1994-01-15. Complete quotient Boolean algebras. https://arxiv.org/abs/math/9401212

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