19 citations · 71 across the 32 of their papers we have counts for
3 papers · 1 filter
Combinatorial properties of non-archimedean convex sets
Artem Chernikov, Alex Mennen
We study combinatorial properties of convex sets over arbitrary valued fields. We demonstrate analogs of some classical results for convex sets over the reals (e.g. the fractional…
Invariant measures in simple and in small theories
Artem Chernikov, Ehud Hrushovski, Alex Kruckman +4
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over the empty set but has mu measure 0 for every automorphism invariant Keisler measur…
Model-theoretic Elekes-Szabó for stable and o-minimal hypergraphs
Artem Chernikov, Ya'acov Peterzil, Sergei Starchenko
A theorem of Elekes and Szabó recognizes algebraic groups among certain complex algebraic varieties with maximal size intersections with finite grids. We establish a generalization…