I have Problems understanding this task:
$\tau=\{X_i : i \in \mathbb{N}\}$.
Prove or disprove that there is a set of first-order sentences $\Phi$, which will be satisfied by an Interpretation $\mathfrak{I}$, if and only if $\mathfrak{I}(Y)=1$ for an infinite set of variables $Y \in \tau$.