Some NIP-like phenomena in NTP$_{2}$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866911278913552384 |
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| author | Kaplan, Itay Simon, Pierre |
| author_facet | Kaplan, Itay Simon, Pierre |
| contents | We introduce the notion of an NTP$_{2}$-smooth measure and prove that they exist assuming NTP$_{2}$. Using this, we propose a notion of distality in NTP$_{2}$ that unfortunately does not intersect simple theories trivially. We then prove a finite alternation theorem for a subclass of NTP$_{2}$ that contains resilient theories. In the last section we prove that under NIP, any type over a model of singular size is finitely satisfiable in a smaller model, and ask if a parallel result (with non-forking replacing finite satisfiability) holds in NTP$_{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1707_05087 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Some NIP-like phenomena in NTP$_{2}$ Kaplan, Itay Simon, Pierre Logic 03C45, 03C95, 03C55 We introduce the notion of an NTP$_{2}$-smooth measure and prove that they exist assuming NTP$_{2}$. Using this, we propose a notion of distality in NTP$_{2}$ that unfortunately does not intersect simple theories trivially. We then prove a finite alternation theorem for a subclass of NTP$_{2}$ that contains resilient theories. In the last section we prove that under NIP, any type over a model of singular size is finitely satisfiable in a smaller model, and ask if a parallel result (with non-forking replacing finite satisfiability) holds in NTP$_{2}$. |
| title | Some NIP-like phenomena in NTP$_{2}$ |
| topic | Logic 03C45, 03C95, 03C55 |
| url | https://arxiv.org/abs/1707.05087 |