An application of Rieger-Nishimura formulas to the intuitionistic modal logics (Q1074572)

Intuitionistic monotone modal logic (imml) is a set of propositional modal formulas containing the usual intuitionistic axioms and closed under modus ponens, substitution and the rule (A\(\to B)/(MA\to MB)\). Extending results of his previous work [ibid. 40, 103-111 (1981; Zbl 0469.03009)], the author proves that for any monadic nonmodal propositional formula A which is derivable classically but not intuitionistically, there is a continuum of immls L such that \(L+A\) is inconsistent. There exists a consistent imml L such that \(L+A\) is inconsistent for any such A. There exist at least countably many immls.