Diagonalization and self-reference

Raymond M. Smullyan

The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. The book provides a survey of introductory material and a summary of recent research. The first chapters are of an introductory nature and consist mainly of exercises with solutions given to most of them.

「Nielsen BookData」より

[目次]

  • I Introduction to Self-Reference and Recursion
  • 1. Introduction to self-reference
  • 2. Some classical fixed point argument compared
  • 3. How to silence a universale machine
  • 4. Some general incompleteness theorems
  • 5. Self-reference in arithmetic
  • 6. Introduction to formal systems and recursion
  • 7. A universal system and its applications
  • II Systems with Effective Properties
  • 8. Arithmetization of formal systems
  • 9. Elementary formal systems and incompleteness proofs
  • 10. Doubly indexed relational systems
  • 11. Effective representation systems
  • III Fixed Point Theorems in a General Setting
  • 12. Sequential systems
  • 13. Strong fixed point properties
  • 14. Multiple fixed point properties
  • 15. Synchronization and pairing functions
  • 16. Some further relations between fixed point properties
  • IV Combinators and Sequential systems
  • 17. Fixed point properties of combinatory logic
  • 18. Formal combinatory logic
  • 19. A second variety of fixed point theorems
  • 20. Extended sequential systems

「Nielsen BookData」より

この本の情報

書名 Diagonalization and self-reference
著作者等 Smullyan, Raymond M
シリーズ名 Oxford logic guides
出版元 Clarendon Press
刊行年月 1994
ページ数 xv, 396 p.
大きさ ill. : 25 cm
ISBN 0198534507
NCID BA23453799
※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