Author: Robert L. Causey
Publisher: Jones & Bartlett Learning
ISBN: 9780763737849
Category : Computers
Languages : en
Pages : 536
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Book Description
The new Second Edition incorporates a wealth of exercise sets, allowing students to test themselves and review important topics discussed throughout the text."--Jacket.
Author: Robert I. Soare
Publisher: Springer Science & Business Media
ISBN: 9783540152996
Category : Mathematics
Languages : en
Pages : 460
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Book Description
..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988
Author: Gerald E. Sacks
Publisher: Cambridge University Press
ISBN: 1107168430
Category : Computers
Languages : en
Pages : 361
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Book Description
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Author: Joseph R. Shoenfield
Publisher: CRC Press
ISBN: 1351419412
Category : Mathematics
Languages : en
Pages : 93
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Book Description
This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.
Author: Piergiorgio Odifreddi
Publisher:
ISBN: 9780444589439
Category : Recursion theory
Languages : en
Pages : 668
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Book Description
Author: David Makinson
Publisher: Springer Science & Business Media
ISBN: 1447125002
Category : Computers
Languages : en
Pages : 302
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Book Description
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.
Author: Moshe Machover
Publisher: Cambridge University Press
ISBN: 9780521479981
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
Author: Chi Tat Chong
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311038129X
Category : Mathematics
Languages : en
Pages : 409
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Book Description
This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.
Author: Nigel Cutland
Publisher: Cambridge University Press
ISBN: 9780521294652
Category : Computers
Languages : en
Pages : 268
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Book Description
What can computers do in principle? What are their inherent theoretical limitations? The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function - a function whose values can be calculated in an automatic way.
Author: Herbert B. Enderton
Publisher: Academic Press
ISBN: 0123849594
Category : Mathematics
Languages : en
Pages : 193
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Book Description
Computability Theory: An Introduction to Recursion Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way. - Frequent historical information presented throughout - More extensive motivation for each of the topics than other texts currently available - Connects with topics not included in other textbooks, such as complexity theory
