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Silvia Barbina (The Open University)

Category
Models and Sets Seminar
Date
Date
Wednesday 24 March 2021
Category

Model theory of Steiner triple systems

A Steiner triple system (STS) is a set together with a collection $B$ of subsets of size 3 such that any two elements of the set belong to exactly one subset in $B$. Finite STSs are well known combinatorial objects for which the literature is extensive. Far fewer results have been obtained on their infinite counterparts, which are natural candidates for model-theoretic investigation. I shall review some constructions of infinite STSs, including the Fraïssé limit of the class of finite STSs. I will then give an axiomatisation of the theory of the Fraïssé limit and describe some of its properties. This is joint work with Enrique Casanovas.