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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 74956
• Item Type
• Journal Item
• ISSN
• 0097-3165
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Travel to Australia	EP/M016242/1	EPSRC Engineering and Physical Sciences Research Council
  Not Set	DP150100506	Australian Research Council (ARC)
  Not Set	FT160100048	Australian Research Council (ARC)

• Keywords
• Steiner triple system; Partial Steiner triple system; Homogeneous; Ultrahomogeneous; Embedding; Subsystem; Fraïssé limit; Countably infinite Steiner triple system
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2021 Daniel Horsley, © 2021 Bridget S. Webb
• Depositing User
• Bridget Webb