Countable homogeneous Steiner triple systems avoiding
specified subsystems

Horsley, Daniel and Webb, Bridget S. (2021). Countable homogeneous Steiner triple systems avoiding
specified subsystems. Journal of Combinatorial Theory, Series A, 180, article no. 105434.

DOI: https://doi.org/10.1016/j.jcta.2021.105434

Abstract

In this article we construct uncountably many new homogeneous locally finite Steiner triple systems of countably infinite order as Fraïssé limits of classes of finite Steiner triple systems avoiding certain subsystems. The construction relies on a new embedding result: any finite partial Steiner triple system has an embedding into a finite Steiner triple system that contains no nontrivial proper subsystems that are not subsystems of the original partial system. Fraïssé’s construction and its variants are rich sources of examples that are central to model-theoretic classification theory, and recently infinite Steiner systems obtained via Fraïssé-type constructions have received attention from the model theory community.

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