Non-Denumerable Infinitary Modal Logic

Segerberg established an analogue of the canonical model theorem in modal logic for infinitary modal logic. However, the logics studied by Segerberg and Goldblatt are based on denumerable sets of pairs 〈Γ, α〉 of sets Γ of well-formed formulae and well-formed formulae α. In this paper I show how a generalisation of the infinite cut-rule used by Segerberg and Goldblatt enables the removal of the limitation to denumerable sets of sequents.