---
tag: W9M8GJP8VE
kind: concept
name: Büchi arithmetic
sources:
  - wikipedia: en:36262566@r1165013864
    locator: Büchi arithmetic
    note: adopted
    mention: wikipedia://en/36262566
    sections: [Summary]
same_as:
  wikidata: Q5005255
  wikipedia: Büchi arithmetic
inventory: [BREWC4FKAS]
---

## Summary

**Büchi arithmetic** of base *k* is the first-order theory of the [[natural numbers|0MWKJ44V5A]] with addition and the function $V_k(x)$ which is defined as the largest power of *k* dividing *x*, named in honor of the Swiss mathematician Julius Richard Büchi. The signature of Büchi arithmetic contains only the addition operation, $V_k$ and equality, omitting the multiplication operation entirely.