MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1243

Preprint Number 1243

Previous Next Preprint server


1243. Alex Kruckman, Nicholas Ramsey
Generic expansion and Skolemization in NSOP_1 theories
E-mail:

Submission date: 20 June 2017

Abstract:

We study expansions of NSOP_1 theories that preserve NSOP_1. We prove that if T is a model complete NSOP_1 theory eliminating the quantifier ∃^∞, then the generic expansion of T by arbitrary constant, function, and relation symbols is still NSOP_1. We give a detailed analysis of the special case of the theory of the generic L-structure, the model companion of the empty theory in an arbitrary language L. Under the same hypotheses, we show that T may be generically expanded to an NSOP_1 theory with built-in Skolem functions. In order to obtain these results, we establish strengthenings of several properties of Kim-independence in NSOP_1 theories, adding instances of algebraic independence to their conclusions.

Mathematics Subject Classification: 03C45, 03C10

Keywords and phrases:

Full text arXiv 1706.06616: pdf, ps.


Last updated: July 3 2017 14:07 Please send your corrections to: