Definable sets in Skolem arithmetic

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Autore principale:	Kamiński, Łukasz
Natura:	Preprint
Pubblicazione:	2025
Soggetti:	Logic
Accesso online:	Acceder al recurso
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_version_	1866914071744348160
author	Kamiński, Łukasz
author_facet	Kamiński, Łukasz
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2510_02062
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Definable sets in Skolem arithmetic Kamiński, Łukasz Logic 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.
title	Definable sets in Skolem arithmetic
topic	Logic
url	https://arxiv.org/abs/2510.02062

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