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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Limitations on representing $\mathcal {P}(X)$ as a union of proper subalgebras
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by L. Š. Grinblat PDF
Proc. Amer. Math. Soc. 143 (2015), 859-868 Request permission

Abstract:

For every integer $\mu \geqslant 3$, there exists a function $f_\mu :\mathbb N^+\rightarrow \mathbb N^+$ such that the following holds: (1) $f_\mu (k)=2k-\mu$ for $k$ large enough; (2) if $\mathfrak A$ is a finite nonempty collection of subalgebras of $\mathcal P(X)$ such that $\bigcap \mathfrak B$ is not $f_\mu \left (\#(\mathfrak B)\right )$-saturated, for all nonempty $\mathfrak B\subseteq \mathfrak A$, then $\bigcup \mathfrak A\neq \mathcal P(X)$.
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Additional Information
  • L. Š. Grinblat
  • Affiliation: Department of Mathematics, Ariel University of Samaria, P.O. Box 3, Ariel 40700, Israel
  • Email: grinblat@ariel.ac.il
  • Received by editor(s): July 17, 2011
  • Received by editor(s) in revised form: July 16, 2012, and April 4, 2013
  • Published electronically: October 27, 2014
  • Communicated by: Julia Knight
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 859-868
  • MSC (2010): Primary 03E05; Secondary 54D35
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12220-9
  • MathSciNet review: 3283672