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Classical Recursion Theory
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Book Synopsis Classical Recursion Theory by : P. Odifreddi
Download or read book Classical Recursion Theory written by P. Odifreddi and published by Elsevier. This book was released on 1992-02-04 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
Book Synopsis Classical recursion theory : the theory of functions and sets of natural numbers by : Piergiorgio Odifreddi
Download or read book Classical recursion theory : the theory of functions and sets of natural numbers written by Piergiorgio Odifreddi and published by . This book was released on 1999 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical recursion theory : the theory of functions and sets of natural numbers by : Piergiorgio Odifreddi
Download or read book Classical recursion theory : the theory of functions and sets of natural numbers written by Piergiorgio Odifreddi and published by . This book was released on 1989 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical Recursion Theory by : Piergiorgio Odifreddi
Download or read book Classical Recursion Theory written by Piergiorgio Odifreddi and published by Elsevier Health Sciences. This book was released on 1989 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
Download or read book Recursion Theory written by Chi Tat Chong and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-08-17 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classical Recursion Theory by : Piergiorgio Odifreddi
Download or read book Classical Recursion Theory written by Piergiorgio Odifreddi and published by Elsevier Health Sciences. This book was released on 1989 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
Book Synopsis Higher Recursion Theory by : Gerald E. Sacks
Download or read book Higher Recursion Theory written by Gerald E. Sacks and published by Cambridge University Press. This book was released on 2017-03-02 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Book Synopsis Theory of Recursive Functions and Effective Computability by : Hartley Rogers (Jr.)
Download or read book Theory of Recursive Functions and Effective Computability written by Hartley Rogers (Jr.) and published by . This book was released on 1967 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Turing Computability by : Robert I. Soare
Download or read book Turing Computability written by Robert I. Soare and published by Springer. This book was released on 2016-06-20 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classical Recursion Theory by : Piergiorgio Odifreddi
Download or read book Classical Recursion Theory written by Piergiorgio Odifreddi and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical Recursion Theory by : Piergiorgio Odifreddi
Download or read book Classical Recursion Theory written by Piergiorgio Odifreddi and published by . This book was released on 1989 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of the study of classical recursion theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The text ends with a treatment of the enumeration degrees.
Book Synopsis Classical Recursion Theory, Volume II by : P. Odifreddi
Download or read book Classical Recursion Theory, Volume II written by P. Odifreddi and published by North Holland. This book was released on 1999-09-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II of Classical Recursion Theory describes the universe from a local (bottom-upor synthetical) point of view, and covers the whole spectrum, from therecursive to the arithmetical sets.The first half of the book provides a detailed picture of the computablesets from the perspective of Theoretical Computer Science. Besides giving adetailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexityclasses, ranging from small time and space bounds to the elementary functions,with a particular attention to polynomial time and space computability. It alsodeals with primitive recursive functions and larger classes, which are ofinterest to the proof theorist. The second half of the book starts with the classical theory of recursivelyenumerable sets and degrees, which constitutes the core of Recursion orComputability Theory. Unlike other texts, usually confined to the Turingdegrees, the book covers a variety of other strong reducibilities, studyingboth their individual structures and their mutual relationships. The lastchapters extend the theory to limit sets and arithmetical sets. The volumeends with the first textbook treatment of the enumeration degrees, whichadmit a number of applications from algebra to the Lambda Calculus.The book is a valuable source of information for anyone interested inComplexity and Computability Theory. The student will appreciate the detailedbut informal account of a wide variety of basic topics, while the specialistwill find a wealth of material sketched in exercises and asides. A massivebibliography of more than a thousand titles completes the treatment on thehistorical side.
Book Synopsis Recursive Analysis by : R. L. Goodstein
Download or read book Recursive Analysis written by R. L. Goodstein and published by Courier Corporation. This book was released on 2013-01-23 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text by a master in the field covers recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.
Download or read book Computability written by Nigel Cutland and published by Cambridge University Press. This book was released on 1980-06-19 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Higher Recursion Theory by : Gerald E. Sacks
Download or read book Higher Recursion Theory written by Gerald E. Sacks and published by Cambridge University Press. This book was released on 2017-03-02 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computability Theory by : Herbert B. Enderton
Download or read book Computability Theory written by Herbert B. Enderton and published by Academic Press. This book was released on 2010-12-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Descriptive Set Theory by : Yiannis N. Moschovakis
Download or read book Descriptive Set Theory written by Yiannis N. Moschovakis and published by American Mathematical Soc.. This book was released on 2009-06-30 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ``effective'' theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.
