Submission date: 13 October 2013.

Abstract:

(accepted for publication in Fundamenta Mathematicae)
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.

Mathematics Subject Classification: 06E05, 06E25, 03C60, 03C10

Keywords and phrases:

Full text arXiv 1310.3527: pdf, ps.