Proofs and Computations (Perspectives in Logic) 1st Edition by Helmut Schwichtenberg (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “Written by two leading practitioners in the area of formal logic, the book provides a panoramic view of the topic. This reference volume is a must for the bookshelf of every practitioner of formal logic and computer science.” Prahladavaradan Sampath, Computing Reviews Book Description This major graduate-level text provides a detailed, self-contained coverage of proof theory. About the Author Helmut Schwichtenberg is an Emeritus Professor of Mathematics at Ludwig-Maximilians-Universität München. He has recently developed the ‘proof-assistant’ MINLOG, a computer-implemented logic system for proof/program development and extraction of computational content.Stanley S. Wainer is an Emeritus Professor of Mathematics at the University of Leeds and a past-President of the British Logic Colloquium. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an exceptionally well-written, concise – and yet virtually self-contained – account of the theoretical essence of what lies at the intersection of Recursion Theory and Proof Theory. Written for a “mathematically mature” audience, it carefully includes all definitions and is careful to back up all theorems with meticulous proofs. A very small sample of the material covered includes careful proofs of Gödel’s First and Second theorems, various independence proofs (e.g. Goodstein’s Theorem), various formulations of models of computation, and completeness theorems. The book is a treasure house of important and significant results and should be of interest to a large segment of the mathematical community. I can’t recommend this book enough!

Keywords

Free Download Proofs and Computations (Perspectives in Logic) 1st Edition in PDF format
Proofs and Computations (Perspectives in Logic) 1st Edition PDF Free Download
Download Proofs and Computations (Perspectives in Logic) 1st Edition 2012 PDF Free
Proofs and Computations (Perspectives in Logic) 1st Edition 2012 PDF Free Download
Download Proofs and Computations (Perspectives in Logic) 1st Edition PDF
Free Download Ebook Proofs and Computations (Perspectives in Logic) 1st Edition