TITLE: Reducts of omega-categorical structures
SPEAKER: András Pongrácz (Middlesex University)
ABSTRACT:
We study a basic question in model theory: Given a structure F, what are the reducts of F, i.e., the structures with a first-order definition in F? If F is the dense linear order or the random graph, then there are five different structures definable from F, up to first-order interdefinability. Recently, the same notion was characterised for several other omega-categorical structures, such as the random tournament, the generic partially ordered set and the random ordered graph. The techniques applied in these proofs rely deeply on structural Ramsey theory. I am going to give a summary about these results and the proof techniques.