### Complete quotient Boolean Algebras

by Kanamori and Shelah. [KaSh:390]

Transactions American Math Soc, 1995

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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