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arXiv · 2404.13661

Equational theory of ordinals with addition and left multiplication by $\omega$

Christian Choffrut
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Abstract

We show that the equational theory of the structure $\langle \omega^{\omega}: (x,y)\mapsto x+y, x\mapsto \omega x \rangle $ is finitely axiomatizable and give a simple axiom schema when the domain is the set of transfinite ordinals. We give an algorithm that given a pair of terms $(E,F)$ decides in linear time with respect of their common length whether or not $E=F$ is a consequence of the axioms.

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Christian Choffrut. 2024-04-21. Equational theory of ordinals with addition and left multiplication by $\omega$. https://doi.org/10.46298/fi.13734

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