SSAOS 2013 - Maja Pech

Maja Pech: Weakly oligomorphic structures

Abstract:

This talk is a survey on the study of weakly oligomorphic structures. A relational structure is called weakly oligomorphic if for every arity there are finitely many relations that can be defined by sets of positive existential formulae.
It will be shown that the notion of weak oligomorphy naturally arises in the study of relational structures by both model-theoretic and algebraic approach i.e. when the notion of definability coincides with the notion of invariance.
In particular, this is the key property that makes a bridge between endolocal and homomorphism-homogeneous structures.
We also discuss the relationship between weak oligomorphy ant the classical notions of oligomorphy and omega-categoricity.