Enrichments of Boolean algebras: a uniform treatment of some classical and some novel examples


Derakhshan, J
Macintyre, A


Fundamenta Mathematicae

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We give a unified treatment of the model theory of various enrichments of infinite atomic Boolean algebras, with special attention to quantifier eliminations, complete axiomatizations and decidability. A classical example is the enrichment by a predicate for the ideal of finite sets, and a novel one involves predicates giving congruence conditions on the cardinality of finite sets. We focus on three examples, and classify them by expressive power.

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Journal Article