Generic trivializations of geometric theories

摘要

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, the NIP and the NTP_2. In particular, we show that T is strongly minimal, supersimple of SU-rank 1, has the NIP or the NTP_2 exactly when T* has these properties. 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.