Model theory of Steiner triple systems

Barbina, Silvia and Casanovas, Enrique (2019). Model theory of Steiner triple systems. Journal of Mathematical Logic, 20(2), article no. 2050010.

DOI: https://doi.org/10.1142/S0219061320500105

Abstract

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, TP₂, NSOP₁, elimination of hyperimaginaries and weak elimination of imaginaries.

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