19 citations · 71 across the 32 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…
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…
Henselian valued fields and inp-minimality
Artem Chernikov, Pierre Simon
We prove that every ultraproduct of -adics is inp-minimal (i.e., of burden ). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselia…