Abstract

The bimodal provability logics of analysis for ordinary provability and provability by the ω-rule are shown to be fragments of certain ‘polymodal’ logics introduced by G.K. Dzhaparidze. In addition to modal axiom schemes expressing Löb's theorem for the two kinds of provability, the logics treated here contain a scheme expressing that if a statement is consistent, then the statement that it is consistent is provable by the ω-rule