# Proof-Theoretic Modal PA-Completeness II: The Syntactic Countermodel

Paolo Gentilini
Studia Logica: An International Journal for Symbolic Logic
Vol. 63, No. 2 (Sep., 1999), pp. 245-268
Stable URL: http://www.jstor.org/stable/20016086
Page Count: 24

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

Preview not available

## Abstract

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 [9]. Given a sequent S so that $\left|\frac{}{GL-LIN}\right.$ S, [Unrepresentable symbol] 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 G and is a tool of general interest in Provability Logic, that allows some classification in the set of the arithmetical interpretations.

• [245]
• 246
• 247
• 248
• 249
• 250
• 251
• 252
• 253
• 254
• 255
• 256
• 257
• 258
• 259
• 260
• 261
• 262
• 263
• 264
• 265
• 266
• 267
• 268