Logical equations and admissible rules of inference with parameters in modal provability logics

@article{Rybakov1990LogicalEA,
  title={Logical equations and admissible rules of inference with parameters in modal provability logics},
  author={Vladimir V. Rybakov},
  journal={Studia Logica},
  year={1990},
  volume={49},
  pages={215-239}
}
This paper concerns modal logics of provability G6del-L6b system GL and Solovay logic S 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) in GL and S is decidable. Then we get a positive solution to Friedman's prob!em for GL and S. We also show that A. V. Kuznetsov's problem of the existence of finite basis for admissible rules for GL and S has a… CONTINUE READING