Model theory of Steiner triple systems

Journal of Mathematical Logic 20 (2):2050010 (2019)

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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References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
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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Citations of this work

Strongly Minimal Steiner Systems I: Existence.John Baldwin & Gianluca Paolini - 2021 - Journal of Symbolic Logic 86 (4):1486-1507.
Forking, Imaginaries, and Other Features Of.Christian D’elbée - 2021 - Journal of Symbolic Logic 86 (2):669-700.

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