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.
• Version 1994-01-20_10 (19p) published version (17p)

@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}
}