Geodesic
Enrichments of Boolean algebras by Presburger predicates
Jamshid Derakhshan 1   ; Angus Macintyre 2
1 St Hilda’s College University of Oxford Cowley Place Oxford OX4 1DY, UK
2 School of Mathematical Sciences Queen Mary University of London Mile End Road London E1 4NS, UK
Fundamenta Mathematicae, Tome 239 (2017) no. 1, pp. 1-17 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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. Our main enrichment is by a predicate for the ideal of finite sets and predicates for congruence conditions on the cardinalities of finite sets, but we also give new proofs of some classical results. We then classify and compare the expressive power of the enriched theories.
DOI : 10.4064/fm673-1-2017
Keywords: unified treatment model theory various enrichments infinite atomic boolean algebras special attention quantifier eliminations complete axiomatizations decidability main enrichment predicate ideal finite sets predicates congruence conditions cardinalities finite sets proofs classical results classify compare expressive power enriched theories

Jamshid Derakhshan  1   ; Angus Macintyre  2

1 St Hilda’s College University of Oxford Cowley Place Oxford OX4 1DY, UK
2 School of Mathematical Sciences Queen Mary University of London Mile End Road London E1 4NS, UK 
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Jamshid Derakhshan; Angus Macintyre. Enrichments of Boolean algebras by Presburger predicates. Fundamenta Mathematicae, Tome 239 (2017) no. 1, pp. 1-17. doi: 10.4064/fm673-1-2017

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