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 Fraisse limit MF. Here, we show that the theory T*Sq of MF is the model completion of the theory of STSs. We also prove that T*Sq is not small and it has quantifier elimination, TP2, NSOP1, elimination of hyperimaginaries and weak elimination of imaginaries.