Fundamentals of Generalized Recursion Theory PDF Download

Author: M. Fitting
Publisher: Elsevier
ISBN: 0080960316
Category : Mathematics
Languages : en
Pages : 329

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Book Description
Fundamentals of Generalized Recursion Theory

Author: Melvin Fitting
Publisher: Elsevier
ISBN: 0444861718
Category : Recursion theory
Languages : en
Pages : 329

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Book Description
Provability, Computability and Reflection.

Author: Jens E. Fenstad
Publisher: Cambridge University Press
ISBN: 1107168163
Category : Mathematics
Languages : en
Pages : 238

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Book Description
This volume presents a unified and coherent account of the many and various parts of general recursion theory.

Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080954898
Category : Computers
Languages : en
Pages : 465

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Book Description
Generalized Recursion Theory

Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 9780080955025
Category : Mathematics
Languages : en
Pages : 416

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Book Description
Provability, Computability and Reflection

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: 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: 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: Jens Erik Fenstad
Publisher:
ISBN: 9780720422009
Category : Recursion theory
Languages : en
Pages : 456

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Book Description

Author: Robert I. Soare
Publisher: Springer
ISBN: 3642319335
Category : Computers
Languages : en
Pages : 289

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Book Description
Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.