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An Isaac Newton Institute Workshop

An Introduction to Recent Applications of Model Theory

Reconstruction of homogeneous relational structures

Author: Silvia Barbina (University of Turin)

Abstract

Reconstruction results give conditions under which the automorphism group of a structure determines the structure up to bi-interpretability or bi-definability. Here we examine a large class of omega-categorical combinatorial structures, which was isolated by Herwig and contains K_n-free graps, k-hypergraphs and Henson digraphs. Using a Baire category approach we show how to obtain reconstruction for this class, proving that a reconstruction condition, developed by M. Rubin, holds. The method rests on the existence of a generic pair of automorphisms.