English

The elementary theory of free Steiner triple systems

Logic 2026-02-25 v2

Abstract

Free Steiner triple systems (STS) are infinite structures that are naturally characterised by a universal property. We consider the class of free STSs from a model theoretic viewpoint. We show that free STSs on any number of generators are elementarily equivalent. We axiomatise their theory and show that it is stable.

Keywords

Cite

@article{arxiv.2411.13723,
  title  = {The elementary theory of free Steiner triple systems},
  author = {Silvia Barbina and Enrique Casanovas},
  journal= {arXiv preprint arXiv:2411.13723},
  year   = {2026}
}