Friday, May 9, 201412:30 pmModel theory seminarGC6417

VC-dimension in model theory and other subjects

Artem Chernikov

Université Paris Diderot - Paris 7

Artem Chernikov

Finite VC-dimension, a combinatorial property of families of
sets, was discovered simultaneously by Vapnik and Chervonenkis in the
context of probabilistic learning theory, and by Shelah in model
theory in the context of classification of unstable first-order
theories (where it is called NIP). From the model theoretic point of
view it is a very attractive setting generalizing stability and
o-minimality, and admitting a deep theory which had been recently used
to study ordered and valued fields. I will give an overview of some
results around NIP related to set theory (counting Dedekind cuts in
infinite linear orders), topological dynamics and compression schemes
in computational learning theory.