Boolean algebras admitting a countable minimally acting group

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.

A rigid Boolean algebra that admits the elimination of Q21

H. Mildenberg (1993)

Fundamenta Mathematicae

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Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier $Q_{1}^{2}$ .

Problems in Boolean algebras

R. Bonnet (1976)

Annales scientifiques de l'Université de Clermont. Mathématiques

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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.