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It is a well-known idea to embed the intuitionistic logic into the modal logic in order to interprete the modality 'provable' as the deducibility in the Peano arithmetics with also well-known difficulties. P. M. Solovay and A. V. Kuznetsov introduced into consideration the Gödel-Löb provability logic whose formulas are constructed from propositional variables with the use of the connectives &amp;, v, ⊃, ¬, and Δ (Gödelised provability). This logic is defined by the classic propositional calculus complemented by the three Δ-axioms

A formal reduction of the general problem of expressibility of formulas in the Gödel-Löb provability logic