A simplified proof of arithmetical completeness theorem for provability logic GLP
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We present a simplified proof of Japaridze’s arithmetical completeness theorem for the well-known polymodal provability logic GLP. The simplification is achieved by employing a fragment J of GLP that enjoys a more convenient Kripke-style semantics than the logic considered in the papers by Ignatiev and Boolos. In particular, this allows us to simplify the arithmetical fixed point construction and to bring it closer to the standard construction due to Solovay.
KeywordsSTEKLOV Institute Kripke Model Axiom Schema Modal Formula Kripke Frame
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