The Unprovability of Consistency: An Essay in Modal Logic
Cambridge University Press, 3/9/2009
EAN 9780521092975, ISBN10: 0521092973
Paperback, 196 pages, 21.6 x 14 x 1.2 cm
Language: English
The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields.
1. G and other normal modal propositional logics
2. Peano Arithmetic
3. The box as Bew
4. Some applications of G
5. Semantics for G and other modal logics
6. Canonical models
7. The completeness and decidability of G
8. Trees for G
9. Calculating the truth-values of fixed points
10. Rosser's theorem
11. The fixed-point theorem
12. Solovay's completeness theorems
13. An S4-preserving proof-theoretical treatment of modality
14. The Craig Interpolation Lemma for G.