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Preprint Number 1433

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1433. Silvia Barbina and Enrique Casanovas
Model theory of Steiner triple systems

Submission date: 17 May 2018


A Steiner triple system 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 \mathcal{B}. It is well known that the class of finite Steiner triple systems 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 Steiner triple systems. We also prove that T^*_{Sq} has quantifier elimination, it is not small and has TP_2 and NSOP_1.

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Full text arXiv 1805.06767: pdf, ps.

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