Generic generalized Rosser fixed points

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.This paper supersedes: Franco Montagna, Extremely undecidable sentences and generic generalized Rosser's fixed points, Rapporto Matematico, No. 95, Siena, 1983.