Extreme types and extremal models
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929210350632960 |
|---|---|
| author | Bagheri, Seyed-Mohammad |
| author_facet | Bagheri, Seyed-Mohammad |
| contents | In the affine fragment of continuous logic, type spaces are compact convex sets. I study some model theoretic properties of extreme types. It is proved that every complete theory $T$ has an extremal model, i.e. a model which realizes only extreme types. Extremal models form an elementary class in the full continuous logic sense if and only if the set of extreme $n$-types is closed in $S_n(T)$ for each $n$. Also, some applications are given in the special cases where the theory has a compact or first order model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extreme types and extremal models Bagheri, Seyed-Mohammad Logic In the affine fragment of continuous logic, type spaces are compact convex sets. I study some model theoretic properties of extreme types. It is proved that every complete theory $T$ has an extremal model, i.e. a model which realizes only extreme types. Extremal models form an elementary class in the full continuous logic sense if and only if the set of extreme $n$-types is closed in $S_n(T)$ for each $n$. Also, some applications are given in the special cases where the theory has a compact or first order model. |
| title | Extreme types and extremal models |
| topic | Logic |
| url | https://arxiv.org/abs/2401.07804 |