A Simplified Proof of Arithmetical Completeness Theorem for Provability Logic GLP
نویسنده
چکیده
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. DOI: 10.1134/S0081543811060046
منابع مشابه
Kripke semantics for provability logic GLP
A well-known polymodal provability logic GLP is complete w.r.t. the arithmetical semantics where modalities correspond to reflection principles of restricted logical complexity in arithmetic [9, 5, 8]. This system plays an important role in some recent applications of provability algebras in proof theory [2, 3]. However, an obstacle in the study of GLP is that it is incomplete w.r.t. any class ...
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