Classical Recursion Theory

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Classical Recursion Theory

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Author : P. Odifreddi
language : en
Publisher: Elsevier
Release Date : 1992-02-04

Classical Recursion Theory written by P. Odifreddi and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-04 with Computers categories.

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.

Classical Recursion Theory

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Author : Piergiorgio Odifreddi
language : en
Publisher:
Release Date : 1989

Classical Recursion Theory written by Piergiorgio Odifreddi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Recursion theory categories.

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.

Higher Recursion Theory

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Author : Gerald E. Sacks
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02

Higher Recursion Theory written by Gerald E. Sacks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Computers categories.

This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.

Computability

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Author : Nigel Cutland
language : en
Publisher: Cambridge University Press
Release Date : 1980-06-19

Computability written by Nigel Cutland and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-06-19 with Computers categories.

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.

Proofs And Computations

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Author : Helmut Schwichtenberg
language : en
Publisher: Cambridge University Press
Release Date : 2011-12-15

Proofs And Computations written by Helmut Schwichtenberg and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-15 with Mathematics categories.

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.

Recursion Theory

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Author : Chi Tat Chong
language : en
Publisher: Walter de Gruyter
Release Date : 2015

Recursion Theory written by Chi Tat Chong and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Computers categories.

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

Descriptive Set Theory

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Author : Yiannis N. Moschovakis
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-31

Descriptive Set Theory written by Yiannis N. Moschovakis and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-31 with Mathematics categories.

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.

Computational Complexity

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Author : Sanjeev Arora
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-20

Computational Complexity written by Sanjeev Arora and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Computers categories.

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Classical Recursion Theory

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Author : Piergiorgio Odifreddi
language : en
Publisher: Elsevier Health Sciences
Release Date : 1989

Classical Recursion Theory written by Piergiorgio Odifreddi and has been published by Elsevier Health Sciences this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Computers categories.

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.