Enrichments of Boolean Algebras: a uniform treatment of some classical and some novel examples
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...
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| Formato: | Journal article |
| Publicado: |
2013
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| Summary: | 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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