Handbook of computability theory
Part 1: Fundamentals of Computability Theory. -- Part 2: Reducibilities and Degrees. -- Part 3: Generalized Computability Theory. -- Part 4: Mathematics and Computability Theory. -- Part 5: Logic and Computability Theory. -- Part 6: Computer Science and Computability Theory
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| Other Authors: | |
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| Format: | Edited Volume |
| Language: | English |
| Published: |
Amsterdam
Elsevier Science & Technology
1999
Amsterdam [u.a.] Elsevier 1999 |
| Edition: | 1. ed |
| Series: | Studies in logic and the foundations of mathematics
140 |
| In: |
Studies in logic and the foundations of mathematics (140)
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| Volumes / Articles: | Show Volumes / Articles. |
| Subjects: | |
| Online Access: | Verlag, Volltext: http://www.sciencedirect.com/science/book/9780444898821 Verlag, Zentralblatt MATH, Inhaltstext: https://zbmath.org/?q=an:0923.03001 
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| Author Notes: | ed. by Edward R. Griffor |
| Summary: | Part 1: Fundamentals of Computability Theory. -- Part 2: Reducibilities and Degrees. -- Part 3: Generalized Computability Theory. -- Part 4: Mathematics and Computability Theory. -- Part 5: Logic and Computability Theory. -- Part 6: Computer Science and Computability Theory The history and concpt of computability / R.I. Soare -- Recursively bounded (r.b.) classes in recursion theory / D. Cenzer -- Reducibilities / P. Odifreddi -- Local degree theory / S.B. Cooper -- The global structure of the Turing degrees / T.A. Slaman -- The recursively enumerable degrees / R.A. Shore -- An overview of the computably enumerable sets / R.I. Soare -- The continuous functionals / D. Normann -- Ordinal recursion theory / C.T. Chong and S.D. Friedman -- E-recursion / G.E. Sacks -- Recursion on abstract structures / P.G. Hinman -- Computable rings and fields / V. Stoltenberg-Hansen and J.V. Tucker -- The structure of computability in analysis and physical theory : an extension of Church's thesis / M.B. Pour-El -- Theory of numberings / Y.L. Ershov -- Pure recursive model theory / T.S. Millar -- Classifying recursive functions / H. Schwichtenberg -- Computation models and function algebras / P. Clote -- Polynomial time reducibilities and degrees / K. Ambos-Spies The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers |
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| Item Description: | Includes bibliographical references and indexes. - Description based on print version record |
| Physical Description: | Online Resource |
| ISBN: | 0444898824 9780080533049 0080533043 9780444898821 |