5 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…
Definable convolution and idempotent Keisler measures III. Generic stability, generic transitivity, and revised Newelski's conjecture
Artem Chernikov, Kyle Gannon, Krzysztof KrupiÅski
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…
On n-dependent groups and fields III. Multilinear forms and invariant connected components
Artem Chernikov, Nadja Hempel
We develop some model theory of multi-linear forms, generalizing Granger in the bi-linear case. In particular, after proving a quantifier elimination result, we show that for an NI…