Characterizations of monadic NIP
Abstract
We give several characterizations of when a complete first-order theory is monadically NIP, i.e. when expansions of 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.
Keywords
Cite
@article{arxiv.2104.12989,
title = {Characterizations of monadic NIP},
author = {Samuel Braunfeld and Michael C. Laskowski},
journal= {arXiv preprint arXiv:2104.12989},
year = {2026}
}
Comments
We include corrigenda to v2 in an appendix. The notion of endless indiscernible triviality is introduced and replaces indiscernible triviality throughout, in particular in Theorem 1.1. The claim regarding the failure of 4-wqo in Theorem 1.2 is withdrawn and remains unproved