Weakly o-minimal types
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910028297928704 |
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| author | Moconja, Slavko Tanović, Predrag |
| author_facet | Moconja, Slavko Tanović, Predrag |
| contents | We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every relatively $L_{\mathfrak{C}}$-definable subset of $p(\mathfrak{C})$ has finitely many convex components in $(p(\mathfrak{C}),<)$. We establish many nice properties of weakly o-minimal types. For example, we prove that weakly o-minimal types are dp-minimal and share several properties of weight-one types in stable theories, and that a version of monotonicity theorem holds for relatively definable functions on the locus of a weakly o-minimal type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08260 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly o-minimal types Moconja, Slavko Tanović, Predrag Logic We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every relatively $L_{\mathfrak{C}}$-definable subset of $p(\mathfrak{C})$ has finitely many convex components in $(p(\mathfrak{C}),<)$. We establish many nice properties of weakly o-minimal types. For example, we prove that weakly o-minimal types are dp-minimal and share several properties of weight-one types in stable theories, and that a version of monotonicity theorem holds for relatively definable functions on the locus of a weakly o-minimal type. |
| title | Weakly o-minimal types |
| topic | Logic |
| url | https://arxiv.org/abs/2404.08260 |