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

05/08/2018

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by   Alexis Bès, et al.

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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 λ less than ε_0, the existential theory of the set of successor ordinals less than λ equipped with multiplication is decidable.