Finite model property for negative modalities

We prove that the logic $N^{Un}$ with negation as unnecessity operator and that its extension, a Heyting–Ockham logic $N^*$, have the finite model property and prove the analog of Dziobiak's theorem for extensions of these logics. Namely, we prove that an extension of $N^{Un}$ or $N^*$ is strongly complete wrt the class of finite frames iff it is tabular.