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arXiv · 2609.01230

The Composition Lemma for $n$-dependence

Artem Chernikov·Yuyan He
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Abstract

We prove that a relation obtained by composing arbitrary functions of arity $\leq k$ with a relation definable in an $n$-dependent structure is $kn$-dependent. This confirms a conjecture of Chernikov and Hempel. We also demonstrate optimality of the result.

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Artem Chernikov, Yuyan He. 2026-09-01. The Composition Lemma for $n$-dependence. https://arxiv.org/abs/2609.01230

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