A note on $\varepsilon$-stability
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915008714113024 |
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| author | Chavarria, Nicolas |
| author_facet | Chavarria, Nicolas |
| contents | We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for $\varepsilon$-stability and briefly discuss finitely satisfiable types. We then do a short survey of $\varepsilon$-stability in a theory. Finally, we consider the map that takes each formula to its "degree" of stability in a given theory and show that it is a seminorm. All of this is done in the context of a first-order formalism that allows predicates to take values in arbitrary compact metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04903 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on $\varepsilon$-stability Chavarria, Nicolas Logic 03C66, 03C45 We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for $\varepsilon$-stability and briefly discuss finitely satisfiable types. We then do a short survey of $\varepsilon$-stability in a theory. Finally, we consider the map that takes each formula to its "degree" of stability in a given theory and show that it is a seminorm. All of this is done in the context of a first-order formalism that allows predicates to take values in arbitrary compact metric spaces. |
| title | A note on $\varepsilon$-stability |
| topic | Logic 03C66, 03C45 |
| url | https://arxiv.org/abs/2411.04903 |