# Sh:390

- Kanamori, A., & Shelah, S. (1995).
*Complete quotient Boolean algebras*. Trans. Amer. Math. Soc.,**347**(6), 1963–1979. arXiv: math/9401212 DOI: 10.2307/2154916 MR: 1282888 -
Abstract:

For I a proper, countably complete ideal on {\mathcal P}(X) for some set X, can the quotient Boolean algebra {\mathcal 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 {\mathcal P}(\kappa ) containing all singletons. In this paper we provide consequences from and consistency results about completeness. - published version (17p)

Bib entry

@article{Sh:390, author = {Kanamori, Akihiro and Shelah, Saharon}, title = {{Complete quotient Boolean algebras}}, journal = {Trans. Amer. Math. Soc.}, fjournal = {Transactions of the American Mathematical Society}, volume = {347}, number = {6}, year = {1995}, pages = {1963--1979}, issn = {0002-9947}, mrnumber = {1282888}, mrclass = {03E35 (03E40 03E55 06E05)}, doi = {10.2307/2154916}, note = {\href{https://arxiv.org/abs/math/9401212}{arXiv: math/9401212}}, arxiv_number = {math/9401212} }