Proofs and computations

Helmut Schwichtenberg, Stanley S. Wainer

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 Godel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to PI11-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 PI11-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.

「Nielsen BookData」より

[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<omega and PI11-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.

「Nielsen BookData」より

この本の情報

書名 Proofs and computations
著作者等 Association for Symbolic Logic
Schwichtenberg, Helmut
Wainer, S. S
Wainer Stanley S. (University of Leeds)
シリーズ名 Perspectives in logic
出版元 Cambridge University Press
刊行年月 2012
ページ数 xiii, 465 p.
大きさ 25 cm
ISBN 9780521517690
NCID BB08096296
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想