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...
| Main Authors: | , |
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| Format: | Journal article |
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2013
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| _version_ | 1826289050777026560 |
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| author | Derakhshan, J Macintyre, A |
| author_facet | Derakhshan, J Macintyre, A |
| author_sort | Derakhshan, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T02:23:00Z |
| format | Journal article |
| id | oxford-uuid:a49a704d-9bcd-4c9f-ba4c-49f4dcb8911a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:23:00Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:a49a704d-9bcd-4c9f-ba4c-49f4dcb8911a2022-03-27T02:34:56ZEnrichments of Boolean Algebras: a uniform treatment of some classical and some novel examplesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a49a704d-9bcd-4c9f-ba4c-49f4dcb8911aSymplectic Elements at Oxford2013Derakhshan, JMacintyre, AWe 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. |
| spellingShingle | Derakhshan, J Macintyre, A Enrichments of Boolean Algebras: a uniform treatment of some classical and some novel examples |
| title | Enrichments of Boolean Algebras: a uniform treatment of some classical
and some novel examples |
| title_full | Enrichments of Boolean Algebras: a uniform treatment of some classical
and some novel examples |
| title_fullStr | Enrichments of Boolean Algebras: a uniform treatment of some classical
and some novel examples |
| title_full_unstemmed | Enrichments of Boolean Algebras: a uniform treatment of some classical
and some novel examples |
| title_short | Enrichments of Boolean Algebras: a uniform treatment of some classical
and some novel examples |
| title_sort | enrichments of boolean algebras a uniform treatment of some classical and some novel examples |
| work_keys_str_mv | AT derakhshanj enrichmentsofbooleanalgebrasauniformtreatmentofsomeclassicalandsomenovelexamples AT macintyrea enrichmentsofbooleanalgebrasauniformtreatmentofsomeclassicalandsomenovelexamples |