A. Chernikov

activity

20092026

most citedHypergraph regularity and higher arity VC-dimension

2 citations · 3 across the 5 of their papers we have counts for

collaborators

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3 papers · 1 filter

math.LO2026

The Composition Lemma for $n$ -dependence

Artem Chernikov, Yuyan He

We prove that a relation obtained by composing arbitrary functions of arity $\leq k$ with a relation definable in an $n$ -dependent structure is $k n$ -dependent. This confirms a conj…

math.LO2026

SOP $_{2}$ =SOP $_{3}$

Artem Chernikov

The classes of SOP $_{2}$ and SOP $_{3}$ first-order theories coincide. This answers a question of Džamonja and Shelah from 2004.

math.LO2026

Combinatorics in one-based and related structures

Artem Chernikov, Sergei Starchenko

We consider some extremal combinatorial questions for bipartite graphs definable in stable one-based (and related) structures. We show that they satisfy both strong Erdős-Hajnal pr…

The Composition Lemma for n-dependence

SOP2​=SOP3​

Combinatorics in one-based and related structures

The Composition Lemma for $n$ -dependence

SOP $_{2}$ =SOP $_{3}$