Proofs and computations
著者
書誌事項
Proofs and computations
（Perspectives in logic）
Cambridge University Press, 2012
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- Preface
- Preliminaries
- Part I. Basic Proof Theory and Computability: 1. Logic
- 2. Recursion theory
- 3. Godel's theorems
- Part II. Provable Recursion in Classical Systems: 4. The provably recursive functions of arithmetic
- 5. Accessible recursive functions, ID< and 11-CA0
- Part III. Constructive Logic and Complexity: 6. Computability in higher types
- 7. Extracting computational content from proofs
- 8. Linear two-sorted arithmetic
- Bibliography
- Index.
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