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arXiv · 1805.03028

Decidability of the existential fragment of some infinitely generated trace monoids: an application to ordinals

Alexis Bès·Christian Choffrut
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Abstract

Diekert, Matiyasevich and Muscholl proved that the existential first-order theory of a trace monoid over a finite alphabet is decidable. We extend this result to a natural class of trace monoids with infinitely many generators. As an application, we prove that for every ordinal $\lambda$ less than $\varepsilon_0$, the existential theory of the set of successor ordinals less than $\lambda$ equipped with multiplication is decidable.

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Alexis Bès, Christian Choffrut. 2018-05-08. Decidability of the existential fragment of some infinitely generated trace monoids: an application to ordinals. https://arxiv.org/abs/1805.03028

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