arXiv:1310.3527 Abstract | arXiv Analytics

arXiv:1310.3527 [math.LO]Abstract References Reviews Resources

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

Published 2013-10-13Version 1

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.

Categories: math.LO

Subjects: 06E05, 06E25, 03C60, 03C10

Keywords: uniform treatment, novel examples, enrichment, infinite atomic boolean algebras, finite sets

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