Abstract
To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is obtained for LR.
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This paper supersedes: Franco Montagna, Extremely undecidable sentences and generic generalized Rosser's fixed points, Rapporto Matematico, No. 95, Siena, 1983.
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de Jongh, D.H.J., Montagna, F. Generic generalized Rosser fixed points. Stud Logica 46, 193–203 (1987). https://doi.org/10.1007/BF00370381
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DOI: https://doi.org/10.1007/BF00370381