Partition algebras for almost-disjoint families
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- by James E. Baumgartner and Martin Weese PDF
- Trans. Amer. Math. Soc. 274 (1982), 619-630 Request permission
Abstract:
A set $a \subseteq \omega$ is a partitioner of a maximal almost-disjoint faculty $F$ of subsets of $\omega$ if every element of $F$ is almost contained in or almost-disjoint from $a$. The partition algebra of $F$ is the quotient of the Boolean algebra of partitioners modulo the ideal generated by $F$ and the finite sets. We show that every countable algebra is a partition algebra, and that CH implies every algebra of cardinality $\leq {2^{{\aleph _0}}}$ is a partition algebra. We also obtain consistency and independence results about the representability of Boolean algebras as partition algebras.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 274 (1982), 619-630
- MSC: Primary 03E05; Secondary 03E50, 06E05
- DOI: https://doi.org/10.1090/S0002-9947-1982-0675070-X
- MathSciNet review: 675070