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

Jamshid Derakhshan; Angus Macintyre

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arXiv · 1310.3527

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

Jamshid Derakhshan·Angus Macintyre

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Abstract

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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BibTeX RIS

Jamshid Derakhshan, Angus Macintyre. 2013-10-13. Enrichments of Boolean Algebras: a uniform treatment of some classical and some novel examples. https://arxiv.org/abs/1310.3527

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