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Preprint Number 1670

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1670. Elisabeth Bouscaren, Bradd Hart, Ehud Hrushovski and Michael C. Laskowski
Non-locally modular regular types in classifiable theories

Submission date: 24 October 2019


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. Moverover, 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.

Mathematics Subject Classification: 03C45

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Full text arXiv 1910.11404: pdf, ps.

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