7 papers
Higher-arity PAC learning, VC dimension and packing lemma
Artem Chernikov, Henry Towsner
The aim of this note is to overview some of our work in Chernikov, Towsner'20 (arXiv:2010.00726) developing higher arity VC theory (VC dimension), including a generalization of…
Averages of hypergraphs and higher arity stability
Artem Chernikov, Henry Towsner
We show that -ary functions giving the measure of the intersection of multi-parametric families of sets in probability spaces, e.g. $(x,y,z) \in X \times Y \times Z \mapsto μ(P_…
Externally definable fsg groups in NIP theories
Artem Chernikov
We show that every fsg group externally definable in an NIP structure is definably isomorphic to a group interpretable in it. Our proof relies on honest definitions and a group chu…
On n-dependent groups and fields III. Multilinear forms and invariant connected components
Artem Chernikov, Nadja Hempel
We develop some model theory of multilinear forms, generalizing Granger's work in the bilinear case. In particular, after proving a quantifier elimination result, we show that for…
Intersecting sets in probability spaces and Shelah's classification
Artem Chernikov, Henry Towsner
For and , given a sufficiently long sequence of events in a probability space all of measure at least , some of them will have…
Definable convolution and idempotent Keisler measures III. Generic stability, generic transitivity, and revised Newelski's conjecture
Artem Chernikov, Kyle Gannon, Krzysztof Krupiński
We study idempotent measures and the structure of the convolution semigroups of measures over definable groups. We isolate the property of generic transitivity and demonstrate that…
Perfect stable regularity lemma and slice-wise stable hypergraphs
Artem Chernikov, Henry Towsner
We investigate various forms of (model-theoretic) stability for hypergraphs and their corresponding strengthenings of the hypergraph regularity lemma with respect to partitions of…