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arXiv · 2104.12989

Characterizations of monadic NIP

Samuel Braunfeld·Michael C. Laskowski
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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.

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Samuel Braunfeld, Michael C. Laskowski. 2021-04-27. Characterizations of monadic NIP. https://doi.org/10.1090/btran%2F94%2010.1090%2Fbtran%2F209

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