4 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 multi-linear forms, generalizing Granger in the bi-linear case. In particular, after proving a quantifier elimination result, we show that for an NI…