caa a22 4500 465779549 CHVBK 20180323111951.0 cr unu---uuuuu 170327e19900601xx s 000 0 eng 10.1007/BF00935600 doi (NATIONALLICENCE)springer-10.1007/BF00935600 Rybakov V. Mathematical Department of Krasnojarsk State University, pr. Svobodnyi 79, 660062, Krasnojarsk, USSR aut Logical equations and admissible rules of inference with parameters in modal provability logics [Elektronische Daten] [V. Rybakov] This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman's problem forGL andS. We also show that A. V. Kuznetsov's problem of the existence of finite basis for admissible rules forGL andS has a negative solution. Afterwards we give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions. Polish Academy of Sciences, 1990 Studia Logica Kluwer Academic Publishers 49/2(1990-06-01), 215-239 0039-3215 49:2<215 1990 49 11225 https://doi.org/10.1007/BF00935600 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00935600 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rybakov V. Mathematical Department of Krasnojarsk State University, pr. Svobodnyi 79, 660062, Krasnojarsk, USSR aut NATIONALLICENCE 773 0- Studia Logica Kluwer Academic Publishers 49/2(1990-06-01), 215-239 0039-3215 49:2<215 1990 49 11225 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer