September 20
Matěj Konečný,
Charles University
Extending partial automorphisms of structures
This is based on joint work with David Evans, Jan Hubička and Jaroslav Nešetřil. The extension property for partial automorphisms (EPPA), also called the Hrushovski property is a property of classes of finite structures stating that for every A there is B containing A as a substructure such that every isomorphism of substructures of A extends to an automorphism of B. Every class with EPPA is an amalgamation class, in fact, EPPA is equivalent to some properties of the automorphism group of the Fraisse limit of the class. In particular, EPPA is a key ingredient in proving ample generics, the small index property etc. In this talk, we show a new easy way of proving EPPA for the class of all finite graphs and then explain how to extend these techniques to get EPPA for two-graph and also the strongest sufficient condition for EPPA so far. This talk should be self-contained.