Christian Choffrut - Equational theory of ordinals with addition and left multiplication by $ω$

fi:13734 - Fundamenta Informaticae, July 5, 2025, Volume 194, Issue 1 - https://doi.org/10.46298/fi.13734
Equational theory of ordinals with addition and left multiplication by $ω$Article

Authors: Christian Choffrut

    We show that the equational theory of the structure $\langle ω^ω: (x,y)\mapsto x+y, x\mapsto ωx \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.


    Volume: Volume 194, Issue 1
    Published on: July 5, 2025
    Accepted on: April 21, 2025
    Submitted on: June 7, 2024
    Keywords: Logic

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