The seminar meets on Wednesday February 13th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jan Hubička — Combinatorial proofs of the extension property for partial automorphisms
Class K of finite structures has extension property for partial automorphisms (EPPA) if for every A in K there exists B in K such that every partial automorphism of A (that is isomorphism of two substructures of A) extends to automorphism of B. Hrushovski, in 1992,
shown that the class of all finite graphs has EPPA. This result was used by Hodges, Hodkinson, Lascar and Shelah to show that the random
graph has small index property. This motivated search for new classes with EPPA. I will show (and partly prove) new general theorem giving a structural condition for class having EPPA. The theorem is a strengthening of the Herwig–Lascar theorem, but the proof techniques are new, combinatorial and completely self-contained.
I will also discuss connection to structural Ramsey theory.
This is joint work with Jaroslav Nesetril and Matej Konecny.