Definability and Scott rank in separable Metric structures
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916465834196992 |
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| author | Bejarano, Diego |
| author_facet | Bejarano, Diego |
| contents | We give a notion of Scott rank for separable metric structures based on the definability of the (metric closures of) automorphism orbits in continuous infinitary logic. This is a continuous analogue of work of Montalbán for countable structures. In the process, we prove some results concerning definability, type omitting, and back-and-forth for metric structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Definability and Scott rank in separable Metric structures Bejarano, Diego Logic We give a notion of Scott rank for separable metric structures based on the definability of the (metric closures of) automorphism orbits in continuous infinitary logic. This is a continuous analogue of work of Montalbán for countable structures. In the process, we prove some results concerning definability, type omitting, and back-and-forth for metric structures. |
| title | Definability and Scott rank in separable Metric structures |
| topic | Logic |
| url | https://arxiv.org/abs/2411.01017 |