The cardinality of reduced power set algebras
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- by Alan D. Taylor PDF
- Proc. Amer. Math. Soc. 103 (1988), 277-280 Request permission
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
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 277-280
- MSC: Primary 03E05; Secondary 06E05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938683-4
- MathSciNet review: 938683