Non-locally modular regular types in classifiable theories

Fuente: arXiv
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Autori principali: Bouscaren, Elisabeth, Hart, Bradd, Hrushovski, Ehud, Laskowski, Michael C.
Natura: Preprint
Pubblicazione: 2019
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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