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The foundations of computability theory

Robic, Borut.

The foundations of computability theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	The foundations of computability theoryby Borut Robic.
Author:	Robic, Borut.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg :2015.
Description:	xx, 331 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Computable functions.
Online resource:	http://dx.doi.org/10.1007/978-3-662-44808-3
ISBN:	9783662448083$q(electronic bk.)

The foundations of computability theory
Robic, Borut.

The foundations of computability theory[electronic resource] /by Borut Robic. - Berlin, Heidelberg :Springer Berlin Heidelberg :2015. - xx, 331 p. :ill., digital ;24 cm.

Introduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert's Attempt at Recovery -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving the Incomputability -- Computation with External Help -- Degrees of Unsolvability -- The Turing Hierarchy of Unsolvability -- The Class D of Degrees of Unsolvability -- C.E. Degrees and the Priority Method -- The Arithmetical Hierarchy -- Further Reading -- App. A, Mathematical Background -- References -- Index.

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.

ISBN: 9783662448083$q(electronic bk.)

Standard No.: 10.1007/978-3-662-44808-3doiSubjects--Topical Terms:

190932
Computable functions.

LC Class. No.: QA9.59

Dewey Class. No.: 511.352

The foundations of computability theory
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505 0 $a Introduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert's Attempt at Recovery -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving the Incomputability -- Computation with External Help -- Degrees of Unsolvability -- The Turing Hierarchy of Unsolvability -- The Class D of Degrees of Unsolvability -- C.E. Degrees and the Priority Method -- The Arithmetical Hierarchy -- Further Reading -- App. A, Mathematical Background -- References -- Index.
520 $a This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.
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