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arXiv · 2209.05120

Existential characterizations of monadic NIP

Samuel Braunfeld·Michael C. Laskowski
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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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Samuel Braunfeld, Michael C. Laskowski. 2025-12-10. Existential characterizations of monadic NIP. https://doi.org/10.1090/cams%2F62

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