A note on the interpretability logic of finitely axiomatized theories

✍ Scribed by Maarten Rijke

• Publisher: Springer Netherlands
• Year: 1991
• Tongue: English
• Weight: 481 KB
• Volume: 50
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00370185

✦ Synopsis

Ill [6]

Albert Visser shows that ILP completely axiomatizes all schemata about provabihty and relative interpretability that are provable in finitely axiomatized theories. In this paper we introduce a system called ILP ~ that completely axiomatizes the arithmetically valid principles of provability in and interpretabihty over such theories. To prove the arithmetical completeness of ILP ~ we use a suitable kind of tail models; as a byproduct we obtain a somewhat modified proof of Visser's completeness result.

1. Q C_ w 2 is transitive, irreflexive and tree-like; 2. P _C Q is given by a set X C_ w such that 0 E X, and ~Py r ~Qy and y 6 X, and such that y 6 X, yPz implies yQz'Pz, for some z';