Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Sole Distributors for the Usa and Canada, Elsevier Science Pub. Co. (1989)
Volume II of Classical Recursion Theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side.
|Categories||categorize this paper)|
|Buy the book||$185.36 used $2000.00 new Amazon page|
|Call number||QA9.6.O35 1989|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Vojtěch Kolman (2010). Continuum, Name and Paradox. Synthese 175 (3):351 - 367.
Andrzej Wiśniewski & Jerzy Pogonowski (2010). Diagonalization in Double Frames. Logica Universalis 4 (1):31-39.
Charles M. Harris (2012). Badness and Jump Inversion in the Enumeration Degrees. Archive for Mathematical Logic 51 (3-4):373-406.
Charles M. Harris (2010). Goodness in the Enumeration and Singleton Degrees. Archive for Mathematical Logic 49 (6):673-691.
Klaus Ambos-Spies, Philipp Bodewig, Yun Fan & Thorsten Kräling (2013). The Partial Orderings of the Computably Enumerable ibT-Degrees and Cl-Degrees Are Not Elementarily Equivalent. Annals of Pure and Applied Logic 164 (5):577-588.
Similar books and articles
Raymond M. Smullyan (1993). Recursion Theory for Metamathematics. Oxford University Press.
Nigel Cutland (1980). Computability, an Introduction to Recursive Function Theory. Cambridge University Press.
Herbert B. Enderton (2011). Computability Theory: An Introduction to Recursion Theory. Academic Press.
Erich Grädel & Yuri Gurevich (1995). Tailoring Recursion for Complexity. Journal of Symbolic Logic 60 (3):952-969.
Robert E. Byerly (1982). An Invariance Notion in Recursion Theory. Journal of Symbolic Logic 47 (1):48-66.
Robert I. Soare (1996). Computability and Recursion. Bulletin of Symbolic Logic 2 (3):284-321.
Jeremy Avigad (2002). An Ordinal Analysis of Admissible Set Theory Using Recursion on Ordinal Notations. Journal of Mathematical Logic 2 (01):91-112.
Iraj Kalantari & Allen Retzlaff (1979). Recursive Constructions in Topological Spaces. Journal of Symbolic Logic 44 (4):609-625.
Robert E. Byerly (1982). Recursion Theory and the Lambda-Calculus. Journal of Symbolic Logic 47 (1):67-83.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Recent downloads (6 months)0
How can I increase my downloads?