  B\"uchi arithmetics $\mathop{\mathbf{BA}}\nolimits_n$, $n\ge 2$, are
extensions of Presburger arithmetic with an unary functional symbol $V_n(x)$
denoting the largest power of $n$ that divides $x$. A rank of a linear order is
the minimal number of condensations required to reach a finite order. We show
that linear orders of arbitrarily large finite rank can be interpreted in
$\mathop{\mathbf{BA}}\nolimits_n$. We also prove that the extension of the
axioms of Presburger arithmetic with the inductive definition of $V_n$ does not
yield an axiomatization of $\mathop{\mathbf{BA}}\nolimits_n$.
