Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Goedel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to 11-CA0. Ordinal analysis and the (Schwichtenberg-Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and 11-CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
- ISBN:
- 9780521517690
- 9780521517690
-
Category:
- Mathematical logic
- Format:
- Hardback
- Publication Date:
-
15-12-2011
- Language:
- English
- Publisher:
- Cambridge University Press
- Country of origin:
- United Kingdom
- Pages:
- 480
- Dimensions (mm):
- 236x160x30mm
- Weight:
- 0.86kg
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