The Unprovability of Consistency
An Essay in Modal Logic
George Boolos(Author)
Cambridge University Press
Published on 30. April 1979
Book
Hardback
208 pages
978-0-521-21879-5 (ISBN)
Article exhausted; check for reprint
Description
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.
More details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Dimensions
Height: 210 mm
Width: 138 mm
Thickness: 20 mm
Weight
415 gr
ISBN-13
978-0-521-21879-5 (9780521218795)
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Content
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.