The logic of \Pi 1 -conservativity continued, Archiv fur Mathematische Logik und Grundlagenforschung (1992)

by P H' ajek, F Montagna, P
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Interpretability logic

by Albert Visser - Mathematical Logic, Proceedings of the 1988 Heyting Conference , 1990
"... Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbert-style programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength ..."
Abstract - Cited by 27 (9 self) - Add to MetaCart
Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbert-style programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength of theories, or better to prove

The Logic of Provability

by Giorgi Japaridze, Dick De Jongh , 1997
"... Contents 1. Introduction, Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . 360 2. Modal logic preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 3. Proof of Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4. Fixed poi ..."
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Contents 1. Introduction, Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . 360 2. Modal logic preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 3. Proof of Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4. Fixed point theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 5. Propositional theories and Magari-algebras . . . . . . . . . . . . . . . . . . . . . 368 6. The extent of Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . 369 7. Classification of provability logics . . . . . . . . . . . . . . . . . . . . . . . . . . 371 8. Bimodal and polymodal provability logics . . . . . . . . . . . . . . . . . . . . . 374 9. Rosser orderings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 10.