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Preprint Number 1243

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1243. Alex Kruckman, Nicholas Ramsey
Generic expansion and Skolemization in NSOP_1 theories

Submission date: 20 June 2017


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

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Full text arXiv 1706.06616: pdf, ps.

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