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 “”.
M. Sambasiva Rao, Abd El-Mohsen Badawy (2014)
Discussiones Mathematicae - General Algebra and Applications
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Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of is obtained.
Ivan Chajda, Radomír Halaš, Josef Zedník (1998)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Bordalo, G. (1980)
Portugaliae mathematica
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Ivan Chajda (2014)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We prove that a certain identity introduced by R. Halaš for classifying basic algebras can be used for characterizing orthomodular lattices in the class of ortholattices with antitone involutions on every principal filter.
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...