Ultrafilters on ω

Journal of Symbolic Logic 60 (2):624-639 (1995)
We study the I-ultrafilters on ω, where I is a collection of subsets of a set X, usually R or ω 1 . The I-ultrafilters usually contain the P-points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist
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Jörg Brendle (2006). Van Douwen's Diagram for Dense Sets of Rationals. Annals of Pure and Applied Logic 143 (1):54-69.
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