19 citations · 53 across the 15 of their papers we have counts for
4 papers · 1 filter
Cutting lemma and Zarankiewicz's problem in distal structures
Artem Chernikov, David Galvin, Sergei Starchenko
We establish a cutting lemma for definable families of sets in distal structures, as well as the optimality of the distal cell decomposition for definable families of sets on the p…
A note on o-minimal flows and the Ax--Lindemann--Weierstrass theorem for abelian varieties over
Ya'acov Peterzil, Sergei Starchenko
In this short note we present an elementary proof of the Ax-Lindemann-Weierstrass theorem for abelian and semi-abelian varieties. The proof uses ideas of Pila, Ullmo, Yafaev, Zanni…
Ramsey growth in some NIP structures
Artem Chernikov, Sergei Starchenko, Margaret E. M. Thomas
We investigate bounds in Ramsey's theorem for relations definable in NIP structures. Applying model-theoretic methods to finitary combinatorics, we generalize a theorem of Bukh and…
Definable regularity lemmas for NIP hypergraphs
Artem Chernikov, Sergei Starchenko
We present a systematic study of the regularity phenomena for NIP hypergraphs and connections to the theory of (locally) generically stable measures, providing a model-theoretic hy…