Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The number of nonisomorphic Boolean subalgebras of a power set


Author: Francisco J. Freniche
Journal: Proc. Amer. Math. Soc. 91 (1984), 199-201
MSC: Primary 06E05; Secondary 03G05
MathSciNet review: 740170
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if $ \kappa $ is an infinite cardinal, then there are $ {2^{{2^\kappa }}}$ nonisomorphic Boolean subalgebras of $ \mathcal{P}\left( \kappa \right)$. Also it is shown that if $ \kappa = c$, then the above subalgebras can be choosen countably complete. This solves a question raised by S. Ulam.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06E05, 03G05

Retrieve articles in all journals with MSC: 06E05, 03G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740170-X
PII: S 0002-9939(1984)0740170-X
Keywords: Boolean algebra, almost disjoint family, large oscillation family
Article copyright: © Copyright 1984 American Mathematical Society