A new proof of the fixed-point theorem of provability logic.
Lisa Reidhaar-Olson · Notre Dame Journal of Formal Logic · 1989
In this paper we give a simple semantic proof of the fixed-point theorem of the modal system G (also known as GL, PRL, L, and K4W).This proof is modeled after a syntactic proof of Sambin's found in Sambin and Valentini [10], yet is simpler than his, due to our taking advantage of the Kripke semantics for G.Other semantic proofs of the theorem exist, e.g. in Gleit [6] and Goldfarb and Gleit [7]; however, the advantages of this particular version are that it is less complicated and the fixed-point so obtained has the same general "appearance" as the original formula.The author wishes to thank George Boolos for guidance and helpful discussions.