Generic trivializations of geometric theories | Zendy

Berenstein Alexander | Zendy; Vassiliev Evgueni | Zendy

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Generic trivializations of geometric theories

Author(s) -

Berenstein Alexander,

Vassiliev Evgueni

Publication year - 2014

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.201300030

Subject(s) - mathematics , nip , converse , rank (graph theory) , simplicity , stability (learning theory) , pure mathematics , discrete mathematics , combinatorics , geometry , computer science , philosophy , epistemology , machine learning , programming language

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.

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