The seminar meets on Wednesday September 5th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Wislaw Kubis — Uniformly homogeneous structures
A structure is homogeneous if every isomorphism between its finitely
generated substructures extends to an automorphism. We shall discuss a
stronger property. Namely, a structure U is uniformly homogeneous if it
is homogeneous and moreover for every finitely generated substructure A
of U there exists a group embedding e : Aut(A) –> Aut(U) such that e(f)
extends f for every f in Aut(A).
Most of the well known homogeneous structures are uniformly homogeneous.
We shall present examples showing that uniform homogeneity is strictly
stronger than homogeneity.
Some of the results are joint with S. Shelah, some other with B.