Büchi arithmetic of base k is the first-order theory of the natural numbers with addition and the function V k ( x ) {\displaystyle 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 {\displaystyle V_{k}} and equality, omitting the multiplication operation entirely.
Büchi arithmetic of base k is the first-order theory of the natural numbers with addition and the function V k ( x ) {\displaystyle 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 {\displaystyle V_{k}} and equality, omitting the multiplication operation entirely.
Source: Wikipedia "Büchi arithmetic" · CC BY-SA 4.0
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