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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: 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: 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: 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: Gerald E. Sacks
Publisher: Cambridge University Press
ISBN: 1316739465
Category : Mathematics
Languages : en
Pages : 362
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Book Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, α-recursion, and E-recursion. This text is essential reading for all researchers in the field.
Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 1439864276
Category : Mathematics
Languages : en
Pages : 895
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Book Description
This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
Author: Blake Crouch
Publisher: Ballantine Books
ISBN: 1524759791
Category : Fiction
Languages : en
Pages : 338
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Book Description
NEW YORK TIMES BESTSELLER • From the bestselling author of Dark Matter and the Wayward Pines trilogy comes a relentless thriller about time, identity, and memory—his most mind-boggling, irresistible work to date, and the inspiration for Shondaland’s upcoming Netflix film. “Gloriously twisting . . . a heady campfire tale of a novel.”—The New York Times Book Review NAMED ONE OF THE BEST BOOKS OF THE YEAR BY Time • NPR • BookRiot Reality is broken. At first, it looks like a disease. An epidemic that spreads through no known means, driving its victims mad with memories of a life they never lived. But the force that’s sweeping the world is no pathogen. It’s just the first shock wave, unleashed by a stunning discovery—and what’s in jeopardy is not our minds but the very fabric of time itself. In New York City, Detective Barry Sutton is closing in on the truth—and in a remote laboratory, neuroscientist Helena Smith is unaware that she alone holds the key to this mystery . . . and the tools for fighting back. Together, Barry and Helena will have to confront their enemy—before they, and the world, are trapped in a loop of ever-growing chaos. Praise for Recursion “An action-packed, brilliantly unique ride that had me up late and shirking responsibilities until I had devoured the last page . . . a fantastic read.”—Andy Weir, #1 New York Times bestselling author of The Martian “Another profound science-fiction thriller. Crouch masterfully blends science and intrigue into the experience of what it means to be deeply human.”—Newsweek “Definitely not one to forget when you’re packing for vacation . . . [Crouch] breathes fresh life into matters with a mix of heart, intelligence, and philosophical musings.”—Entertainment Weekly “A trippy journey down memory lane . . . [Crouch’s] intelligence is an able match for the challenge he’s set of overcoming the structure of time itself.”—Time “Wildly entertaining . . . another winning novel from an author at the top of his game.”—AV Club
Author: Raymond M. Smullyan
Publisher: Oxford University Press, USA
ISBN: 019508232X
Category : Computers
Languages : en
Pages : 180
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Book Description
This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
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
Author: Helmut Schwichtenberg
Publisher: Cambridge University Press
ISBN: 1139504169
Category : Mathematics
Languages : en
Pages : 480
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Book Description
Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
