Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 573

Preprint Number 573

Previous Next Preprint server

573. Alexander Berenstein, Evgueni Vassiliev
Generic Trivializations of Geometric Theories

Submission date: 1 April 2013.


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.

Full text: pdf, dvi, ps.

Last updated: April 1 2013 17:55 Please send your corrections to: