# Computability Theory

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- Author : S. Barry Cooper
- Publisher : CRC Press
- Release : 06 September 2017
- ISBN : 9781351991964
- Page : 420 pages
- Rating : 4.5/5 from 103 voters

## Computability Theory Book PDF summary

Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability 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 book 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 and lively way.

### Computability Theory

- Author : S. Barry Cooper
- Publisher : CRC Press
- Release Date : 2017-09-06
- ISBN : 9781351991964

Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction

### Handbook of Computability Theory

- Author : E.R. Griffor
- Publisher : Elsevier
- Release Date : 1999-10-01
- ISBN : 0080533043

The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey

### Computability Theory

- Author : Herbert B. Enderton
- Publisher : Academic Press
- Release Date : 2010-12-30
- ISBN : 0123849594

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

### Computability Theory and Its Applications

- Author : Peter Cholak,Steffen Lempp,Manuel Lerman,Richard A. Shore
- Publisher : American Mathematical Soc.
- Release Date : 2000
- ISBN : 9780821819227

This collection of articles presents a snapshot of the status of computability theory at the end of the millennium and a list of fruitful directions for future research. The papers represent the works of experts in the field who were invited speakers at the AMS-IMS-SIAM Joint Summer Conference on Computability Theory and Applications held at the University of Colorado (Boulder). The conference focused on open problems in computability theory and on some related areas in which the ideas, methods, and/

### The Foundations of Computability Theory

- Author : Borut Robič
- Publisher : Springer Nature
- Release Date : 2020-11-13
- ISBN : 9783662624210

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

### Logic, Foundations of Mathematics, and Computability Theory

- Author : Robert E. Butts,Jaakko Hintikka
- Publisher : Springer Science & Business Media
- Release Date : 2012-12-06
- ISBN : 9789401011389

The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well,

### Computability Theory And Foundations Of Mathematics - Proceedings Of The 9th International Conference On Computability Theory And Foundations Of Mathematics

- Author : Ningning Peng,Kazuyuki Tanaka,Liang Yu,Guohua Wu
- Publisher : World Scientific
- Release Date : 2022-05-18
- ISBN : 9789811259302

This volume features the latest scientific developments in the fields of computability theory and logical foundations of mathematics as well as applications. The scope involves the topics of Computability Theory, Reverse Mathematics, Nonstandard Analysis, Proof Theory, Set Theory, Philosophy of Mathematics, Constructive Mathematics, Theory of Randomness and Computational Complexity Theory.

### Computability Theory

- Author : Herbert B. Enderton
- Publisher : Unknown
- Release Date : 2011
- ISBN : 0123849586

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

### Computability Theory

- Author : Rebecca Weber
- Publisher : American Mathematical Soc.
- Release Date : 2012
- ISBN : 9780821873922

What can we compute--even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory. The goal of this book is to give the reader a firm grounding in the fundamentals of computability theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools

### The Foundations of Computability Theory

- Author : Borut Robič
- Publisher : Springer
- Release Date : 2015-09-14
- ISBN : 9783662448083

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

### Turing Computability

- Author : Robert I. Soare
- Publisher : Springer
- Release Date : 2016-06-20
- ISBN : 9783642319334

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

### Theories of Computability

- Author : Nicholas Pippenger
- Publisher : Cambridge University Press
- Release Date : 1997-05-28
- ISBN : 0521553806

A mathematically sophisticated introduction to Turing's theory, Boolean functions, automata, and formal languages.

### Computability Theory

- Author : Neil D. Jones
- Publisher : Academic Press
- Release Date : 2014-06-20
- ISBN : 9781483218489

Computability Theory: An Introduction provides information pertinent to the major concepts, constructions, and theorems of the elementary theory of computability of recursive functions. This book provides mathematical evidence for the validity of the Church–Turing thesis. Organized into six chapters, this book begins with an overview of the concept of effective process so that a clear understanding of the effective computability of partial and total functions is obtained. This text then introduces a formal development of the equivalence of Turing

### Models of Computation

- Author : Maribel Fernandez
- Publisher : Springer Science & Business Media
- Release Date : 2009-04-14
- ISBN : 9781848824348

A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: - Automata and Turing Machines; - Recursive functions

### Computability

- Author : Nigel Cutland
- Publisher : Cambridge University Press
- Release Date : 1980-06-19
- ISBN : 0521294657

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.