Unification in subsystem J${}_2$ of provability logic GLB

We generalize methods, developed by S. Ghilardi, and apply them to a subsystem J${}_2$ of bimodal provability logic GLB. We describe projective formulas in J${}_2$ in terms of Kripke semantics and prove that logic J${}_2$ has finitary unification type. As an application, we show that admissibility problem for J${}_2$ is decidable.