Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The cardinality of reduced power set algebras

Author: Alan D. Taylor
Journal: Proc. Amer. Math. Soc. 103 (1988), 277-280
MSC: Primary 03E05; Secondary 06E05
MathSciNet review: 938683
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a general result on the cardinality of reduced powers of structures via filters that has several consequences including the following: if $I$ is a uniform, countably complete ideal on the real line $\mathcal {R}$ and $\mathcal {B}$ is the Boolean algebra of subsets of $\mathcal {R}$ modulo $I$, then $\left | \mathcal {B} \right | > {2^{{\aleph _0}}}$ and if ${2^\nu } \leq {2^{{\aleph _0}}}$ for all $\nu < {2^{{\aleph _0}}}$ then $\left | \mathcal {B} \right | = {2^{{2^{{\aleph _0}}}}}$. This strengthens some results of Kunen and Pelc [7] and Prikry [8] obtained by Boolean ultrapower techniques. Our arguments are all combinatorial and some applications are included.

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

Similar Articles

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

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

Additional Information

Article copyright: © Copyright 1988 American Mathematical Society