Canonical quotients in model theory
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909434241875968 |
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| author | Fernández, Adrián Portillo |
| author_facet | Fernández, Adrián Portillo |
| contents | We study canonical quotients in model theory, mainly stable quotients of type-definable groups and invariant types in NIP theories. We extend the modelling property to continuous theories and use it to study $n$-dependence in hyperdefinable sets. Furthermore, we study maximal WAP and tame quotients of $S_X(\mathfrak{C})$, where $\mathfrak{C}$ is a monster model of a complete theory $T$ and $X$ is an $\emptyset$-type-definable set and show that the Ellis groups of the maximal WAP quotient flow and the maximal tame quotient flow do not depend on the choice of the monster model $\mathfrak{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14862 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canonical quotients in model theory Fernández, Adrián Portillo Logic 03C45 We study canonical quotients in model theory, mainly stable quotients of type-definable groups and invariant types in NIP theories. We extend the modelling property to continuous theories and use it to study $n$-dependence in hyperdefinable sets. Furthermore, we study maximal WAP and tame quotients of $S_X(\mathfrak{C})$, where $\mathfrak{C}$ is a monster model of a complete theory $T$ and $X$ is an $\emptyset$-type-definable set and show that the Ellis groups of the maximal WAP quotient flow and the maximal tame quotient flow do not depend on the choice of the monster model $\mathfrak{C}$. |
| title | Canonical quotients in model theory |
| topic | Logic 03C45 |
| url | https://arxiv.org/abs/2412.14862 |