Proofs and Computations
β Helmut Schwichtenberg, Stanley S. Wainer
π Library
π
2012
π Cambridge University Press
π English
β¦ LIBER β¦
π
Proofs and Computations
β Scribed by Helmut Schwichtenberg, Stanley S. Wainer
- Publisher
- Cambridge University Press
- Year
- 2012
- Tongue
- English
- Leaves
- 482
- Series
- Perspectives in Logic
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
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 GΓΆdel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Ξ 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 Ξ 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.
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