Decidability of the existential fragment of some infinitely generated trace monoids: an application to ordinals
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2018
- DOI:
- 10.48550/arXiv.1805.03028
- arXiv:
- arXiv:1805.03028
- Bibcode:
- 2018arXiv180503028B
- Keywords:
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- Computer Science - Logic in Computer Science;
- Mathematics - Logic