Representing real numbers in denumerable Boolean algebras
William Hanf (1976)
Fundamenta Mathematicae
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William Hanf (1976)
Fundamenta Mathematicae
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Roman Sikorski (1963)
Colloquium Mathematicae
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Roman Sikorski (1961)
Colloquium Mathematicum
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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.
Roman Sikorski, T. Traczyk (1963)
Colloquium Mathematicum
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Robert Lagrange (1974)
Colloquium Mathematicae
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Paul Iverson (1991)
Colloquium Mathematicae
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There is a conjecture of Vaught [17] which states: Without The Generalized Continuum Hypothesis one can prove the existence of a complete theory with exactly nonisomorphic, denumerable models. In this paper we show that there is no such theory in the class of complete extensions of the theory of Boolean algebras. More precisely, any complete extension of the theory of Boolean algebras has either 1 or nonisomorphic, countable models. Thus we answer this conjecture in the negative...
Abad Manuel, Cimadamore Cecilia, Díaz Varela José (2009)
Open Mathematics
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In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
Miroslav Katětov (1951)
Colloquium Mathematicae
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