Model theory of Steiner triple systems

Journal of Mathematical Logic 20 (2):2050010 (2019)
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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 of M_F is the model completion of the theory of STSs. We also prove that T is not small and it has quantifier elimination, TP2, NSOP1, elimination of hyperimaginaries and weak elimination of imaginaries.

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Citations of this work

Forking, imaginaries, and other features of.Christian D’elbée - 2021 - Journal of Symbolic Logic 86 (2):669-700.
Strongly minimal Steiner systems I: Existence.John Baldwin & Gianluca Paolini - 2021 - Journal of Symbolic Logic 86 (4):1486-1507.
Towards a finer classification of strongly minimal sets.John T. Baldwin & Viktor V. Verbovskiy - 2024 - Annals of Pure and Applied Logic 175 (2):103376.

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References found in this work

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Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
On model-theoretic tree properties.Artem Chernikov & Nicholas Ramsey - 2016 - Journal of Mathematical Logic 16 (2):1650009.
Forking and dividing in NTP₂ theories.Artem Chernikov & Itay Kaplan - 2012 - Journal of Symbolic Logic 77 (1):1-20.
An axiomatic approach to free amalgamation.Gabriel Conant - 2017 - Journal of Symbolic Logic 82 (2):648-671.

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