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.
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}
}