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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Good and OK ultrafilters


Author: Alan Dow
Journal: Trans. Amer. Math. Soc. 290 (1985), 145-160
MSC: Primary 54D35; Secondary 04A20, 06E15
MathSciNet review: 787959
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Abstract: In this paper we extend Kunen's construction of $ {\alpha ^ + }$-good ultrafilters on $ \mathcal{P}(\alpha )$ to more general algebras, as well as the construction of $ {\alpha ^ + }$-OK ultrafilters. In so doing, we prove the existence of $ ({2^\alpha } \times {\alpha ^ + })$-independent matrices, as defined by Kunen, in these algebras. Some of the topological properties of the Stone spaces of these algebras are then investigated. We find points, for example, in $ U(\alpha )$ which can be regarded as a generalization of weak $ P$-points.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0787959-4
PII: S 0002-9947(1985)0787959-4
Keywords: Good ultrafilter, independent matrix, $ U(\alpha )$
Article copyright: © Copyright 1985 American Mathematical Society