Relative Unification in Intuitionistic Logic: Towards provability logic of HA

This paper studies relative unification and admissibility in the intuitionistic logic. We generalize results of [Ghilardi, 1999; Iemhoff, 2001a] and prove them relative in NNIL(par) propositions, the class of propositions with No Nested Implications in the Left made up from parameters. The main application of such generalization is to characterize provability logic of Heyting Arithmetic HA and prove its decidability [Mojtahedi, 2022].