Robic B The Foundations of Computability Theory 2015 torrent

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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.
Table of contents
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 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