On dense subsets of Boolean algebras
Roman Sikorski (1963)
Colloquium Mathematicae
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Roman Sikorski (1963)
Colloquium Mathematicae
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Roman Sikorski (1961)
Colloquium Mathematicum
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Janusz Czelakowski (1981)
Colloquium Mathematicae
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W. Luxemburg (1964)
Fundamenta 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.
Martin Gavalec (1981)
Colloquium Mathematicae
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Paul R. Halmos (1954-1956)
Compositio Mathematica
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Bernhard Banaschewski (1993)
Commentationes Mathematicae Universitatis Carolinae
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The functor taking global elements of Boolean algebras in the topos of sheaves on a complete Boolean algebra is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in -valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial injectives, and (ii) the category of frames has no absolute retracts.
B. Rotman (1972)
Fundamenta Mathematicae
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Saul Kripke (1967)
Fundamenta Mathematicae
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Katarzyna Osiak (2007)
Fundamenta Mathematicae
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Let K be an ordered field. The set X(K) of its orderings can be topologized to make it a Boolean space. Moreover, it has been shown by Craven that for any Boolean space Y there exists a field K such that X(K) is homeomorphic to Y. Becker's higher level ordering is a generalization of the usual concept of ordering. In a similar way to the case of ordinary orderings one can define a topology on the space of orderings of fixed exact level. We show that it need not be Boolean. However, our...