What question did this study set out to answer?

The research aims to explore the implications of a universal theory being not monadically NIP through existential configurations.

February 2, 2026Open Access

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Existential characterizations of monadic NIP

SBSamuel BraunfeldCzech Academy of Sciences, Institute of Computer Science MLM. LaskowskiUniversity of Maryland, College Park

Key Points

The research aims to explore the implications of a universal theory being not monadically NIP through existential configurations.
Analysis of universal theories and their properties regarding monadic NIP
Definition of canonical configurations using existential formulas
Comparison between hereditary classes of relational structures and their stability and NIP statuses
A universal theory that is not monadically NIP is identified through an existential formula.
Hereditary classes are shown to be NIP or stable if they are monadically NIP or monadically stable, respectively.
Classes not monadically NIP demonstrate superexponential growth rates.

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.

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Cite This Study

Braunfeld et al. (Thu,) studied this question.

synapsesocial.com/papers/6980fbe1c1c9540dea80db37 https://doi.org/https://doi.org/10.1090/cams/62

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