Proofs and Computations (Hardcover)
 
作者: Helmut Schwichtenberg 
分類: Mathematical logic  
書城編號: 384616


售價: $1008.00

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出版社: Cambridge University Press
出版日期: 2011/12/15
尺寸: 241x165x32mm
重量: 878 grams
ISBN: 9780521517690
 
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商品簡介
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 G del's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11-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 Π11-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.
Helmut Schwichtenberg 作者作品表

eBook: Logic of Computation (DRM PDF)

eBook: Proof and Computation (DRM PDF)

Proofs and Computations (Hardcover)

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