19 citations · 71 across the 32 of their papers we have counts for
40 papers
Forking in monadically NIP theories
Artem Chernikov
We demonstrate that forking in monadically NIP theories satisfies a very strong form of triviality over arbitrary sets, generalizing Baldwin-Shelah in monadically stable theories a…
A counterexample to Petrykowski's conjecture
Artem Chernikov
We construct a simple expansion of the theory of nonabelian free groups in which the group admits a global type with bounded left-translation orbit but is not definably amenable. T…
The Composition Lemma for -dependence
Artem Chernikov, Yuyan He
We prove that a relation obtained by composing arbitrary functions of arity with a relation definable in an -dependent structure is -dependent. This confirms a conj…
SOP=SOP
Artem Chernikov
The classes of SOP and SOP first-order theories coincide. This answers a question of Džamonja and Shelah from 2004.
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…
Fractional Helly property and combinatorics of forking in NTP theories
Artem Chernikov, Chuyin Jiang
We investigate the class of FHP theories, i.e. theories of structures in which all definable families of sets satisfy the Fractional Helly Property (and its variants) from combinat…