Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.02062 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _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 |