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2026-02-18

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/228722

The elementary theory of free Steiner triple systems

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https://doi.org/10.1017/jsl.2026.10188

Abstract

Free Steiner triple systems (STSs) 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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Combinatòria (Matemàtica), Teoria de models, Lògica matemàtica

Subject (English)

Combinations, Model theory, Mathematical logic

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Articles publicats en revistes (Matemàtiques i Informàtica)

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BARBINA, Silvia and CASANOVAS RUIZ-FORNELLS, Enrique. The elementary theory of free Steiner triple systems. Journal of Symbolic Logic. 2026. ISSN 0022-4812. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/228722

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