Download the fantastic book titled Proofs and Computations written by Helmut Schwichtenberg, available in its entirety in both PDF and EPUB formats for online reading. This page includes a concise summary, a preview of the book cover, and detailed information about "Proofs and Computations", which was released on 15 December 2011. We suggest perusing the summary before initiating your download. This book is a top selection for enthusiasts of the Mathematics genre.
Summary of Proofs and Computations by Helmut Schwichtenberg PDF
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 Gödel'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.
Detail About Proofs and Computations PDF
- Author : Helmut Schwichtenberg
- Publisher : Cambridge University Press
- Genre : Mathematics
- Total Pages : 480 pages
- ISBN : 1139504169
- Release Date : 15 December 2011
- PDF File Size : 33,8 Mb
- Language : English
- Rating : 4/5 from 21 reviews
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