# Abstract In this note* we show that the monadic fragment of $L_{\omega \omega}\left(Q_1\right)$ satisfies the interpolation theorem and is, in fact, a maximal monadic logic satisfying countable compactness and a form of the downward Löwenheim-Skolem theorem down to $\aleph_1$. This is similar to Lindstrom's theorem for $L_{\omega \omega}$, and it follows from the topological properties of the space of models. We introduce monadic filter ${ }^1$ quantifiers and show that they are essentially the cardinal quantifiers (Section 2). A back-and-forth characterization of elementary equivalence is given for those logics obtained by adjoining filter quantifiers to the propositional connectives (Section 3). This is used in Section 4 to show that if two sentences of $L_{\omega \omega}\left(Q_1\right)$ have an interpolant in the infinitary logic $L_{\infty \omega}\left(Q_1\right)$ allowing conjunctions of arbitrary sets of formulas, then they have an interpolant ${ }^2$ in $L_{\omega \omega}\left(Q_1\right)$. Actually, a stronger result is proved: if $L^*$ and $L^{\#}$ are countably compact extensions of $L_{\omega \omega}\left(Q_1\right), L^*$ obtained by adding filter $\omega_1$-complete quantifiers, and $L^* \prec L^{\#}$, then two disjoint $P C$ classes of $L^{\#}$ that can be separated in the infinitary logic $L_{\infty}^*$, can also be separated in $L^*$. With this we may show that $L_{\omega \omega}\left(Q_1\right)$ is a maximal countably compact sublogic of $L_{\infty \omega}\left(Q_1\right)$.