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Overlap Algebras: a Constructive Look at Complete Boolean Algebras [PDF]
Logical Methods in Computer Science, 2020 The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set.
Francesco Ciraulo, Michele Contente
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Some Properties of Complete Boolean Algebras
Sahand Communications in Mathematical Analysis, 2021 Summary: The main result of this paper is a characterization of the strongly algebraically closed algebras in the lattice of all real-valued continuous functions and the equivalence classes of \(\lambda\)-measurable. We shall provide conditions which strongly algebraically closed algebras carry a strictly positive Maharam submeasure.
Али Молхаси
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Simple complete Boolean algebras [PDF]
Proceedings of the American Mathematical Society, 2000 For every regular cardinal κ \kappa there exists a simple complete Boolean algebra with κ \kappa generators.
Thomas Jech, Saharon Shelah
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Complete Boolean Algebras are Bousfield Lattices [PDF]
, 2018 Given a complete Heyting algebra we construct an algebraic tensor triangulated category whose Bousfield lattice is the Booleanization of the given Heyting algebra. As a consequence we deduce that any complete Boolean algebra is the Bousfield lattice of some tensor triangulated category.
Greg Stevenson
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Boolean-valued equivalence relations and complete extensions of complete boolean algebras [PDF]
Bulletin of the Australian Mathematical Society, 1970 It is remarked that, if A is a complete boolean algebra and δ is an A-valued equivalence relation on a non-empty set I, then the set of δ-extensional functions from I to A can be regarded as a complete boolean algebra extension of A and a characterization is given of the complete extensions which arise in this way.
Denis Higgs
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On Countably Closed Complete Boolean Algebras [PDF]
Journal of Symbolic Logic, 1995 AbstractIt is unprovable that every complete subalgebra of a countably closed complete Boolean algebra is countably closed.
Thomas Jech, Saharon Shelah
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Complete Quotient Boolean Algebras [PDF]
Transactions of the American Mathematical Society, 1995 For I I a proper, countably complete ideal on the power set P ( x ) \mathcal {P}(x) for some set X X , can the quotient Boolean algebra P ( X ) / I \mathcal {P}(X)/I
Akihiro Kanamori, Saharon Shelah
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Free complete extensions of Boolean algebras [PDF]
Pacific Journal of Mathematics, 1965 George Day
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A note on complete Boolean algebras [PDF]
Proceedings of the American Mathematical Society, 1958 R. S. Pierce
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MEASURE THEORY OF COMPLETE BOOLEAN ALGEBRAS
Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics, 1952 Minoru Tomita
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