Characterizations of monadic NIP
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910191021195264 |
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| author | Braunfeld, Samuel Laskowski, Michael C. |
| author_facet | Braunfeld, Samuel Laskowski, Michael C. |
| contents | We give several characterizations of when a complete first-order theory $T$ is monadically NIP, i.e. when expansions of $T$ by arbitrary unary predicates do not have the independence property. The central characterization is a condition on finite satisfiability of types. Other characterizations include decompositions of models, the behavior of indiscernibles, and a forbidden configuration. As an application, we prove non-structure results for hereditary classes of finite substructures of non-monadically NIP models that eliminate quantifiers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_12989 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Characterizations of monadic NIP Braunfeld, Samuel Laskowski, Michael C. Logic Combinatorics 03C45 We give several characterizations of when a complete first-order theory $T$ is monadically NIP, i.e. when expansions of $T$ by arbitrary unary predicates do not have the independence property. The central characterization is a condition on finite satisfiability of types. Other characterizations include decompositions of models, the behavior of indiscernibles, and a forbidden configuration. As an application, we prove non-structure results for hereditary classes of finite substructures of non-monadically NIP models that eliminate quantifiers. |
| title | Characterizations of monadic NIP |
| topic | Logic Combinatorics 03C45 |
| url | https://arxiv.org/abs/2104.12989 |