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 “”.
Katětov, M.
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Brian L. Davis, Iwo Labuda (2007)
Mathematica Slovaca
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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.
Jan Waszkiewicz (1970)
Colloquium Mathematicae
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Roland Coghetto (2015)
Formalized Mathematics
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We are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres) and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections).
Kamal Boussaf, Alain Escassut (1995)
Annales mathématiques Blaise Pascal
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