The Logic of Provability

Abstract

1. GL and other systems of propositional modal logic 2. Peano arithmetic 3. The box as Bew(x) 4. Semantics for GL and other modal logics 5. Completeness and decidability of GL and K, K4, T, B, S4, and S5 6. Canonical models 7. On GL 8. The fixed point theorem 9. The arithmetical completeness theorems for GL and GLS 10. Trees for GL 11. An incomplete system of modal logic 12. An S4 -preserving proof-theoretical treatment of modality 13. Modal logic within set theory 14. Modal logic within analysis 15. The joint provability logic of consistency and w-consistency 16. On GLB: the fixed point theorem, letterless sentences, and analysis 18. Quantified provability logic with one one-place predicate letter Notes Bibliography Index.