Good and OK ultrafilters

Dow, Alan

doi:10.1090/S0002-9947-1985-0787959-4

Good and OK ultrafilters
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by Alan Dow PDF

Trans. Amer. Math. Soc. 290 (1985), 145-160 Request permission

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 ${\alpha ^ + }\text {-}\text {OK}$ 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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