Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Kamiński, Łukasz
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414820632
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