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two different intermediate logics whose intersection is Int

Call a partial order $\mathcal{F}=(F, \leq)$ rooted if there is an element $a \in F$ such that for any $b \in F$, $a\leq b$. Let $\mathcal{F}_0$ and $\mathcal{F}_1$ be two different finite rooted par …
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Kripke frame, lattice and some intermediate logics

For a given finite and rooted intuitionistic Kripke frame $\mathcal{F}$, let $\log(\mathcal{F})=\{\phi : \mathcal{F}\vDash \phi\}$ and assume $S=\{\log(\mathcal{F}): \mathcal{F} \text{ is finite and r …
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