Definability in affine continuous logic
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911793292509184 |
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| author | Bagheri, Seyed-Mohammad |
| author_facet | Bagheri, Seyed-Mohammad |
| contents | I study definable sets in affine continuous logic. Let $T$ be an affine theory. After giving some general results, it is proved that if $T$ has a first order model, its extremal theory is a complete first order theory and first order definable sets are affinely definable. In this case, the type spaces of $T$ are Bauer simplices and they coincide with the sets of Keisler measures of the extremal theory. In contrast, if $T$ has a compact model, definable sets are exactly the end-sets of definable predicates. As an example, it is proved in the theory of probability algebras that one dimensional definable sets are exactly the intervals $[a,b]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Definability in affine continuous logic Bagheri, Seyed-Mohammad Logic I study definable sets in affine continuous logic. Let $T$ be an affine theory. After giving some general results, it is proved that if $T$ has a first order model, its extremal theory is a complete first order theory and first order definable sets are affinely definable. In this case, the type spaces of $T$ are Bauer simplices and they coincide with the sets of Keisler measures of the extremal theory. In contrast, if $T$ has a compact model, definable sets are exactly the end-sets of definable predicates. As an example, it is proved in the theory of probability algebras that one dimensional definable sets are exactly the intervals $[a,b]$. |
| title | Definability in affine continuous logic |
| topic | Logic |
| url | https://arxiv.org/abs/2401.07714 |