Infinite products of filters
Brian L. Davis, Iwo Labuda (2007)
Mathematica Slovaca
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Displaying similar documents to “Thin ultrafilters”
Infinite products of filters
Compounding Objects
Zvonimir Šikić (2020)
Bulletin of the Section of Logic
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We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which is actually unconvincing in the case of ultrafilters. As a bonus, we get a very simple proof of Łoś's theorem.
On descriptive classification of functions
Katětov, M.
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Seven characterizations of non-meager 𝖯-filters
Kenneth Kunen, Andrea Medini, Lyubomyr Zdomskyy (2015)
Fundamenta Mathematicae
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We give several topological/combinatorial conditions that, for a filter on ω, are equivalent to being a non-meager -filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a non-meager -filter. Here, we identify a filter with a subspace of through characteristic functions. Along the way, we generalize to non-meager -filters a result of Miller (1984) about -points, and we employ and give a new proof of results of Marciszewski (1998). We also...
Ultrafilter with predecessors in Rudin-Frolík order
Lev Bukovský, Eva Butkovičová (1981)
Commentationes Mathematicae Universitatis Carolinae
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On the extensibility of closed filters in T spaces and the existence of well orderable filter bases
Kyriakos Keremedis, Eleftherios Tachtsis (1999)
Commentationes Mathematicae Universitatis Carolinae
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We show that the statement CCFC = “” is equivalent to the CMC and, the axiom of choice AC is equivalent to the statement CFE = “”. We also show that AC is equivalent to each of the assertions: “”, “” and “”.