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Preprint Number 573

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573. Alexander Berenstein, Evgueni Vassiliev
Generic Trivializations of Geometric Theories
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Submission date: 1 April 2013.

Abstract:

We study the theory T^* of the structure induced by parameter free formulas on a “dense” algebraically independent subset of a model of a geometric theory T. We show that while being a trivial geometric theory, T^* inherits most of the model theoretic complexity of T related to stability, simplicity, rosiness, NIP and NTP_2. In particular, we show that T is strongly minimal, supersimple of SU-rank 1, or NIP exactly when so is T^*. We show that if T is superrosy of thorn rank 1, then so is T^*, and that the converse holds if T satisfies acl=dcl.

Mathematics Subject Classification: 03C10, 03C45, 03C64

Keywords and phrases: geometric theories, strongly minimal theories, supersimple SU-rank one theories, superrosy thorn rank one theories, NIP theories, strongly dependent theories, NTP_2 theories.

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