Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields
We define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multiplicative group of a local field of characteristic zero are finite-by-Presburger and interpret the higher residue rings...
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| Format: | Journal article |
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Cornell University
2016
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| _version_ | 1826256585862676480 |
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| author | Derakhshan, J Macintyre, A |
| author_facet | Derakhshan, J Macintyre, A |
| author_sort | Derakhshan, J |
| collection | OXFORD |
| description | We define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multiplicative group of a local field of characteristic zero are finite-by-Presburger and interpret the higher residue rings of the local field. We apply these results to give a new proof of the model completeness in the ring language of a local field of characteristic zero (a result that follows also from work of Prestel-Roquette). |
| first_indexed | 2024-03-06T18:04:33Z |
| format | Journal article |
| id | oxford-uuid:00ff3f5d-210d-440b-a7bd-4a1d4a54f228 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:04:33Z |
| publishDate | 2016 |
| publisher | Cornell University |
| record_format | dspace |
| spelling | oxford-uuid:00ff3f5d-210d-440b-a7bd-4a1d4a54f2282022-03-26T08:32:29ZModel theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fieldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:00ff3f5d-210d-440b-a7bd-4a1d4a54f228Symplectic Elements at OxfordCornell University2016Derakhshan, JMacintyre, AWe define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multiplicative group of a local field of characteristic zero are finite-by-Presburger and interpret the higher residue rings of the local field. We apply these results to give a new proof of the model completeness in the ring language of a local field of characteristic zero (a result that follows also from work of Prestel-Roquette). |
| spellingShingle | Derakhshan, J Macintyre, A Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields |
| title | Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields |
| title_full | Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields |
| title_fullStr | Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields |
| title_full_unstemmed | Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields |
| title_short | Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields |
| title_sort | model theory of finite by presburger abelian groups and finite extensions of p adic fields |
| work_keys_str_mv | AT derakhshanj modeltheoryoffinitebypresburgerabeliangroupsandfiniteextensionsofpadicfields AT macintyrea modeltheoryoffinitebypresburgerabeliangroupsandfiniteextensionsofpadicfields |