Studia Logica

, Volume 49, Issue 1, pp 7–21

# Decidable and enumerable predicate logics of provability

• Giorgie Dzhaparidze
Article

## Abstract

Predicate modal formulas are considered as schemata of arithmetical formulas, where □ is interpreted as the standard formula of provability in a fixed “sufficiently rich” theory T in the language of arithmetic. QLT(T) and QLT are the sets of schemata of T-provable and true formulas, correspondingly. Solovay's well-known result — construction an arithmetical counterinterpretation by Kripke countermodel — is generalized on the predicate modal language; axiomatizations of the restrictions of QLT(T) and QLT by formulas, which contain no variables different from x, are given by means of decidable prepositional bimodal systems; under the assumption that T is Π1-complete, there is established the enumerability of the restrictions of QLT(T) and QLT by: 1) formulas in which the domains of different occurrences of □ don't intersect and 2) formulas of the form n ⊥ → A.

## Keywords

Mathematical Logic Computational Linguistic Standard Formula Predicate Logic Modal Language
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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