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Classical Recursion Theory, Volume II: Volume 143
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Classical Recursion Theory, Volume II: Volume 143 Hardcover - 1999 - 1st Edition

by P. Odifreddi


From the publisher

Volume II of Classical Recursion Theory describes the universe from a local (bottom-upor synthetical) point of view, and covers the whole spectrum, from therecursive to the arithmetical sets.The first half of the book provides a detailed picture of the computablesets from the perspective of Theoretical Computer Science. Besides giving adetailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexityclasses, ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It alsodeals with primitive recursive functions and larger classes, which are ofinterest to the proof theorist. The second half of the book starts with the classical theory of recursivelyenumerable sets and degrees, which constitutes the core of Recursion orComputability Theory. Unlike other texts, usually confined to the Turingdegrees, the book covers a variety of other strong reducibilities, studyingboth their individual structures and their mutual relationships. The lastchapters extend the theory to limit sets and arithmetical sets. The volumeends with the first textbook treatment of the enumeration degrees, whichadmit a number of applications from algebra to the Lambda Calculus.The book is a valuable source of information for anyone interested inComplexity and Computability Theory. The student will appreciate the detailedbut informal account of a wide variety of basic topics, while the specialistwill find a wealth of material sketched in exercises and asides. A massivebibliography of more than a thousand titles completes the treatment on thehistorical side

First line

As a first approximation, we introduce static complexity measures in an abstract way as follows: given an acceptable system of indices (e)e for the partial recursive functions (see II.5.2), we call a static complexity measure any total recursive function m, and call complexity or size of e the number m(e).

Details

  • Title Classical Recursion Theory, Volume II: Volume 143
  • Author P. Odifreddi
  • Binding Hardcover
  • Edition number 1st
  • Edition 1
  • Pages 949
  • Volumes 1
  • Language ENG
  • Publisher North-Holland
  • Date September 1, 1999
  • Illustrated Yes
  • Features Bibliography, Illustrated, Index, Table of Contents
  • ISBN 9780444502056 / 044450205X
  • Weight 3.65 lbs (1.66 kg)
  • Dimensions 9.1 x 6.4 x 2.5 in (23.11 x 16.26 x 6.35 cm)
  • Library of Congress Catalog Number 88033481
  • Dewey Decimal Code 511.3
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Classical Recursion Theory, Volume II
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Classical Recursion Theory, Volume II

by Odifreddi, P

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Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol. 2 (Studies...
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Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol. 2 (Studies in Logic and the Foundations of Mathematics, Vol. 143)

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Classical Recursion Theory, Vol. 2
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Classical Recursion Theory, Vol. 2

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Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol. 2 (Studies in Logic and the Foundations of Mathematics, Vol. 143) (Volume 143)

by Odifreddi, P

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