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arXiv · 2411.13723

The elementary theory of free Steiner triple systems

Silvia Barbina·Enrique Casanovas
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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.

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Silvia Barbina, Enrique Casanovas. 2024-11-20. The elementary theory of free Steiner triple systems. https://doi.org/10.1017/jsl.2026.10188

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