Non-locally modular regular types in classifiable theories
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866909167958097920 |
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| author | Bouscaren, Elisabeth Hart, Bradd Hrushovski, Ehud Laskowski, Michael C. |
| author_facet | Bouscaren, Elisabeth Hart, Bradd Hrushovski, Ehud Laskowski, Michael C. |
| contents | We introduce the notion of strong $p$-semi-regularity and show that if $p$ is a regular type which is not locally modular then any $p$-semi-regular type is strongly $p$-semi-regular. Moreover, for any such $p$-semi-regular type, "domination implies isolation" which allows us to prove the following: Suppose that $T$ is countable, classifiable and $M$ is any model. If $p\in S(M)$ is regular but not locally modular and $b$ is any realization of $p$ then every model $N$ containing $M$ that is dominated by $b$ over $M$ is both constructible and minimal over $Mb$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_11404 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Non-locally modular regular types in classifiable theories Bouscaren, Elisabeth Hart, Bradd Hrushovski, Ehud Laskowski, Michael C. Logic 03C45 We introduce the notion of strong $p$-semi-regularity and show that if $p$ is a regular type which is not locally modular then any $p$-semi-regular type is strongly $p$-semi-regular. Moreover, for any such $p$-semi-regular type, "domination implies isolation" which allows us to prove the following: Suppose that $T$ is countable, classifiable and $M$ is any model. If $p\in S(M)$ is regular but not locally modular and $b$ is any realization of $p$ then every model $N$ containing $M$ that is dominated by $b$ over $M$ is both constructible and minimal over $Mb$. |
| title | Non-locally modular regular types in classifiable theories |
| topic | Logic 03C45 |
| url | https://arxiv.org/abs/1910.11404 |