Definable sets in Skolem arithmetic
Logic
2025-10-03 v1
Abstract
In this note, we present a characterization of sets definable in Skolem arithmetic, i.e., the first-order theory of natural numbers with multiplication. This characterization allows us to prove the decidability of the theory. The idea is similar to that of Mostowski; however, our characterization is new, and the proof relies on different combinatorial tools. The main goal of this note is to provide a simpler decidability proof than those previously known.
Cite
@article{arxiv.2510.02062,
title = {Definable sets in Skolem arithmetic},
author = {Łukasz Kamiński},
journal= {arXiv preprint arXiv:2510.02062},
year = {2025}
}