On the ideals' extension theorem and its equivalence to the axiom of choice
S. Mrówka (1956)
Fundamenta Mathematicae
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Displaying similar documents to “The boolean prime ideal theorem holds iff maximal open filters exist”
On the ideals' extension theorem and its equivalence to the axiom of choice
On primeness and maximality of filters
Francis Borceux, Maria-Cristina Pedicchio (1989)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Prime filters with CIP
Zdeněk Frolík (1972)
Commentationes Mathematicae Universitatis Carolinae
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Generalized co-annihilator of BL-algebras
Biao Long Meng, Xiao Long Xin (2015)
Open Mathematics
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In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of coannihilator and the set of the form x-1F where F is a filter, and study basic properties of generalized co-annihilators. We also introduce the notion of involutory filters relative to a filter F and prove that the set of all involutory filters relative to a filter with respect to the suit operations is a complete Boolean lattice and BL-algebra. We use the technology of generalized co-annihilators...
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 “”.