The elementary theory of free Steiner triple systems
arXiv:2411.13723 · doi:10.1017/jsl.2026.10188
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.
This is a post-publication version with revised proofs for Proposition 5.13, Proposition 6.4 and Theorem 7.5 (case 3). We have also made minor corrections to Definition 3.6, Remark 4.2(2), the proofs of Proposition 4.7 and Corollary 6.7. Several typos have been corrected