Buss S (Ed ) Handbook of Proof Theory 1998 torrent

Textbook in DJVU format

Proof theory is the study of proofs as formal objects and is concerned with a broad range of related topics. It is one of the central topics of mathematical logic and has applications in many areas of mathematics, philosophy, and computer science.
Historically, proof theory was developed by mathematicians and philosophers as a formalization for mathematical reasoning; however, proof theory has gradually become increasingly important for computer science, and nowadays proof theory and theoretical computer science are recognized as being very closely connected.
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists in proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. We have attempted to include many of the central topics in proof theory; but have opted to have self-contained expository articles, rather than to have encyclopedic coverage. Thus, a number of important topics have been largely omitted, but with the dvantage that the included material is covered in more detail and at greater depth.
Contents:
Preface
List of Contributors
An Introduction to Proof Theory (Samuel R. Buss)
First-Order Proof Theory of Arithmetic (Samuel R. Buss)
Hierarchies of Provably Recursive Functions (Matt Fairtlough and Stanley S. Wainer)
Subsystems of Set Theory and Second Order Number Theory (Wolfram Pohlers)
Godel's Functional ("Dialectica") Interpretation (Jeremy A vigad and Solomon Feferman)
Realizability (Anne S. Troelstra)
The Logic of Provability (Giorgi Japaridze and Dick de Jongh)
The Lengths of Proofs (Pavel Pudlak)
A Proof-Theoretic Framework for Logic Programming (Gerhard Jager and Robert F. Stark)
Types in Logic, Mathematics and Programming (Robert L. Constable)
Name Index
Subject Index