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PreprintarXiv licencearXiv

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 ≤ 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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Cite

BibTeXRIS
BibTeX
@misc{chernikov2026composition,
  title = {{The Composition Lemma for $n$-dependence}},
  author = {Artem Chernikov and Yuyan He},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01230},
  eprint = {2609.01230},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01230},
}
RIS
TY  - UNPB
TI  - The Composition Lemma for n-dependence
AU  - Artem Chernikov
AU  - Yuyan He
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01230
UR  - https://arxiv.org/abs/2609.01230
AB  - We prove that a relation obtained by composing arbitrary functions of arity ≤ 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.
ER  -