Displaying similar documents to “Strongly retractive Boolean algebras”

Another note on countable Boolean algebras

Lutz Heindorf (1996)

Commentationes Mathematicae Universitatis Carolinae

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We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.

The elementary-equivalence classes of clopen algebras of P-spaces

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.

The number of countable isomorphism types of complete extensions of the theory of Boolean algebras

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 ω 1 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 2 ω nonisomorphic, countable models. Thus we answer this conjecture in the negative...