Séminaire Logique mathématique ICJ

N-dependent theories

by Artem Chernikov (UCLA)

Europe/Paris
Salle 112 Bâtiment Braconnier

Salle 112 Bâtiment Braconnier

Description
A first-order theory is n-dependent if the edge relation of an infinite random n-hypergraph is not definable in any of its models. N-dependence is a strict hierarchy increasing with n, with the first level corresponding to the well-studied class of NIP theories. I will give a survey of recent work on n-dependent theories establishing  connections to higher-arity generalizations of VC-dimension and hypergraph regularity (joint with Henry Towsner) and on understanding which algebraic structures are n-dependent (joint with Nadja Hempel).
 
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