Complete quotient Boolean algebras

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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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Logic, General Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/152888

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9401212
 http://arxiv.org/abs/math/9401212
 Trans. Amer. Math. Soc. 347 (1995), 1963--1979

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arXiv