  Given a number field $K$ one associates to it the set $\Lambda_K$ of Dedekind
zeta-functions of finite abelian extensions of $K$. In this short note we
present a proof of the following Theorem: for any number field $K$ the set
$\Lambda_K$ determines the isomorphism class of $K$. This means that if for any
number field $K'$ the two sets $\Lambda_K$ and $\Lambda_{K'}$ coincide, then $K
\simeq K'$. As a consequence of this fact we deduce an alternative approach
towards the proof of Neukirch-Uchida Theorem for the case of non-normal
extensions of number fields.
