Good and OK ultrafilters. (English, English) Zbl 0532.54021

Dow, Alan

Trans. Am. Math. Soc. 290, 145-160 (1985).

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 topolological properties of the Stone space 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.

MSC:

54D35	Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54A25	Cardinality properties (cardinal functions and inequalities, discrete subsets)
06B30	Topological lattices

Keywords:

alpha\(+\)-good ultrafilter; independent matrix; Stone space; generalization of weak P-points

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