Submission date: 27 April 2021

Abstract:

We give several characterizations of when a complete first-order theory T is monadically NIP, i.e. when expansions of T by arbitrary unary predicates do not have the independence property. The central characterization is a condition on finite satisfiability of types. Other characterizations include decompositions of models, the behavior of indiscernibles, and a forbidden configuration. As an application, we prove non-structure results for hereditary classes of finite substructures of non-monadically NIP models that eliminate quantifiers.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 2104.12989: pdf, ps.