A Steiner triple system (STS) is a set S together with a collection a of subsets of S of size 3 such that any two elements of S belong to exactly one element of a. It is well known that the class of finite STS has a Fraïssé limit MF. Here, we show that the theory TSqa - of MF is the model completion of the theory of STSs. We also prove that TSqa - is not small and it has quantifier elimination, TP2, NSOP1, elimination of hyperimaginaries and weak elimination of imaginaries.
Model theory of Steiner triple systems
Barbina S.
;
2020-01-01
Abstract
A Steiner triple system (STS) is a set S together with a collection a of subsets of S of size 3 such that any two elements of S belong to exactly one element of a. It is well known that the class of finite STS has a Fraïssé limit MF. Here, we show that the theory TSqa - of MF is the model completion of the theory of STSs. We also prove that TSqa - is not small and it has quantifier elimination, TP2, NSOP1, elimination of hyperimaginaries and weak elimination of imaginaries.File in questo prodotto:
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