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