Model theory of Steiner triple systems.

A Steiner triple system (STS) is a set S together with a collection ℬ of subsets of S of size 3 such that any two elements of S belong to exactly one element of ℬ. It is well known that the class of finite STS has a Fraïssé limit M F . Here, we show that the theory T Sq ∗ of M F is the model completion of the theory of STSs. We also prove that T Sq ∗ is not small and it has quantifier elimination, TP 2 , NSOP 1 , elimination of hyperimaginaries and weak elimination of imaginaries. [ABSTRACT FROM AUTHOR]