3 problems

Let $n$ be finite, and let ${\operatorname{ILog}}(\omega^n,\preceq)$ denote the intermediate logic of the frame $(\omega^n,\preceq)$. Local finiteness claim. For all finite $n$, ……

Disjunctive-binding decidability conjecture. The fragment $db$ enjoys a decidable satisfiability problem.

Conjunctive-binding positive-properties conjecture. The fragment $cb$ enjoys the finite-model property and has a decidable satisfiability problem.