Proof-Theoretic Modal PA-Completeness II: The Syntactic Countermodel
- Cite this article as:
- Gentilini, P. Studia Logica (1999) 63: 245. doi:10.1023/A:1005266731458
This paper is the second part of the syntactic demonstration of the Arithmetical Completeness of the modal system G, the first part of which is presented in . Given a sequent S so that ⊢GL-LIN S, ⊬G S, and given its characteristic formula H = char(S), which expresses the non G-provability of S, we construct a canonical proof-tree T of ~ H in GL-LIN, the height of which is the distance d(S, G) of S from G. T is the syntactic countermodel of S with respect to Gand is a tool of general interest in Provability Logic, that allows some classification in the set of the arithmetical interpretations.