A Lifting Theorem for Boolean ...-Algebras.
J.D. Maitland Wright (1969)
Mathematische Zeitschrift
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J.D. Maitland Wright (1969)
Mathematische Zeitschrift
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Peter G. Dodds, Ben de Pagter (1984)
Mathematische Zeitschrift
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Robert Lagrange (1974)
Colloquium Mathematicae
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Brian Wynne (2008)
Fundamenta Mathematicae
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Two Boolean algebras are elementarily equivalent if and only if they satisfy the same first-order statements in the language of Boolean algebras. We prove that every Boolean algebra is elementarily equivalent to the algebra of clopen subsets of a normal P-space.
Janusz Czelakowski (1981)
Colloquium Mathematicae
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Janusz Czelakowski (1978)
Colloquium Mathematicae
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Raymond Balbes (1970)
Mathematische Zeitschrift
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Awad A. Iskander (1972)
Mathematische Zeitschrift
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Marek Balcerzak, Artur Bartoszewicz, Piotr Koszmider (2004)
Colloquium Mathematicae
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We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.
Martin Gavalec (1981)
Colloquium Mathematicae
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Alfred L. Foster (1953)
Mathematische Zeitschrift
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Matthew I. Gould, George Grätzer (1967)
Mathematische Zeitschrift
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D. H. Fremlin, B. de Pagter, W. J. Ricker (2005)
Studia Mathematica
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Complete and σ-complete Boolean algebras of projections acting in a Banach space were introduced by W. Bade in the 1950's. A basic fact is that every complete Boolean algebra of projections is necessarily a closed set for the strong operator topology. Here we address the analogous question for σ-complete Boolean algebras: are they always a sequentially closed set for the strong operator topology? For the atomic case the answer is shown to be affirmative. For the general case, we develop...
Roman Sikorski, T. Traczyk (1963)
Colloquium Mathematicum
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