On the existence property over a predicate
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909515120640000 |
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| author | Usvyatsov, Alexander |
| author_facet | Usvyatsov, Alexander |
| contents | We prove that in a countable theory T fully stable over a predicate P, any complete set A has the existence property. This means that A can be extended to a model of T without changing the P-part. In particular, T has the Gaifman property: any model of P occurs as the P-part of some model of T. This generalizes results of Lachlan (on stable theories), Hodges (on relatively categorical abelian groups), and Afshordel (on difference fields of characteristic 0). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence property over a predicate Usvyatsov, Alexander Logic We prove that in a countable theory T fully stable over a predicate P, any complete set A has the existence property. This means that A can be extended to a model of T without changing the P-part. In particular, T has the Gaifman property: any model of P occurs as the P-part of some model of T. This generalizes results of Lachlan (on stable theories), Hodges (on relatively categorical abelian groups), and Afshordel (on difference fields of characteristic 0). |
| title | On the existence property over a predicate |
| topic | Logic |
| url | https://arxiv.org/abs/2502.20236 |