The elementary theory of free Steiner triple systems
Silvia Barbina, Enrique Casanovas
TL;DR
This paper studies free Steiner triple systems from a model-theoretic perspective, showing they are elementarily equivalent regardless of generators, axiomatizing their theory, and proving its stability.
Contribution
It provides a model-theoretic analysis of free Steiner triple systems, including axiomatization and stability results, which is a new approach in this area.
Findings
Free STSs on any number of generators are elementarily equivalent.
The theory of free STSs is axiomatizable.
The theory of free STSs is stable.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.