On Non-Standard Models of Büchi Arithmetics

Büchi arithmetics ${}_n$, $n\ge 2$, are extensions of Presburger arithmetic with an unary functional symbol $V_n(x)$ denoting the largest power of $n$ that divides $x$. We explore the structure of non-standard models of Büchi arithmetics and construct an example of a countable non-standard model of ${}_2$.