caa a22 4500 465779190 CHVBK 20180323111950.0 cr unu---uuuuu 170327e19900301xx s 000 0 eng 10.1007/BF00401550 doi (NATIONALLICENCE)springer-10.1007/BF00401550 Dzhaparidze Giorgie Academy of Sciences of Georgian SSR, Institute of Philosophy, Roustaveli Av. 29, 380009, Tbilisi, USSR aut Decidable and enumerable predicate logics of provability [Elektronische Daten] [Giorgie Dzhaparidze] 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. QL T(T) and QL T 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 QL T(T) and QL T by formulas, which contain no variables different from x, are given by means of decidable prepositional bimodal systems; under the assumption that T is Π 1-complete, there is established the enumerability of the restrictions of QL T(T) and QL T by: 1) formulas in which the domains of different occurrences of □ don't intersect and 2) formulas of the form □ n ⊥ → A. Kluwer Academic Publishers, 1990 Studia Logica Kluwer Academic Publishers 49/1(1990-03-01), 7-21 0039-3215 49:1<7 1990 49 11225 https://doi.org/10.1007/BF00401550 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00401550 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dzhaparidze Giorgie Academy of Sciences of Georgian SSR, Institute of Philosophy, Roustaveli Av. 29, 380009, Tbilisi, USSR aut NATIONALLICENCE 773 0- Studia Logica Kluwer Academic Publishers 49/1(1990-03-01), 7-21 0039-3215 49:1<7 1990 49 11225 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer