Propositional formulas closed in the minimal calculus

The notion of diagnostic propositional formula was introduced by Uspenski as a generalization of the well-known Kolmogorov's result on interconnection between intuitionistic and classical logics. In the present paper, all calculi having diagnostic formulas relative to the minimal calculus are found. By means of the Kripke model technique developed here new proofs of some known results are obtained.