Decidable and enumerable predicate logics of provability |
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Authors: | Giorgie Dzhaparidze |
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Affiliation: | (1) Academy of Sciences of Georgian SSR, Institute of Philosophy, Roustaveli Av. 29, 380009 Tbilisi, USSR |
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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 1-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. |
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