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arXiv · 2006.04605

Countable homogeneous Steiner triple systems avoiding specified subsystems

Daniel Horsley·Bridget S. Webb
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Abstract

In this article we construct uncountably many new homogeneous locally finite Steiner triple systems of countably infinite order as Fra\"{\i}ss\'{e} 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. Fra\"{\i}ss\'e'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 Fra\"{\i}ss\'e-type constructions have received attention from the model theory community.

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BibTeXRIS

Daniel Horsley, Bridget S. Webb. 2020-06-08. Countable homogeneous Steiner triple systems avoiding specified subsystems. https://doi.org/10.1016/j.jcta.2021.105434

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