The Composition Lemma for $n$ -dependence

Artem Chernikov, Yuyan He

Source record

Source: arXiv

Published: Sep 1, 2026

arXiv: 2609.01230

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Source 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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