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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.10506 |
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| _version_ | 1866917328917102592 |
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| author | Yaacov, Itaï Ben Ibarlucía, Tomás |
| author_facet | Yaacov, Itaï Ben Ibarlucía, Tomás |
| contents | We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other fundamental properties of forking calculus. Most notably, stationarity holds over arbitrary sets (in fact, every type is Lascar strong). On the other hand, we prove that stability is preserved under direct integrals of measurable fields of structures. We deduce that stability in the extremal models of an affine theory implies stability of the theory. We also deduce that the affine part of a stable continuous logic theory is affinely stable, generalising the result of preservation of stability under randomisations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability in affine logic Yaacov, Itaï Ben Ibarlucía, Tomás Logic Functional Analysis We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other fundamental properties of forking calculus. Most notably, stationarity holds over arbitrary sets (in fact, every type is Lascar strong). On the other hand, we prove that stability is preserved under direct integrals of measurable fields of structures. We deduce that stability in the extremal models of an affine theory implies stability of the theory. We also deduce that the affine part of a stable continuous logic theory is affinely stable, generalising the result of preservation of stability under randomisations. |
| title | Stability in affine logic |
| topic | Logic Functional Analysis |
| url | https://arxiv.org/abs/2503.10506 |