Existential characterizations of monadic NIP
Logic
2026-02-10 v3 Combinatorics
Abstract
We show that if a universal theory is not monadically NIP, then this is witnessed by a canonical configuration defined by an existential formula. As a consequence, we show that a hereditary class of relational structures is NIP (resp. stable) if and only if it is monadically NIP (resp. monadically stable). As another consequence, we show that if such a class is not monadically NIP, then it has superexponential growth rate.
Keywords
Cite
@article{arxiv.2209.05120,
title = {Existential characterizations of monadic NIP},
author = {Samuel Braunfeld and Michael C. Laskowski},
journal= {arXiv preprint arXiv:2209.05120},
year = {2026}
}
Comments
Accepted version; minor changes; 24 pages