Ordinal Definability And Recursion Theory
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Ordinal Definability and Recursion Theory
Author | : Alexander S. Kechris,Benedikt Löwe,John R. Steel |
Publsiher | : Cambridge University Press |
Total Pages | : 552 |
Release | : 2016-01-11 |
Genre | : Mathematics |
ISBN | : 9781107033405 |
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The third in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
The Cabal Seminar
Author | : Alexander S. Kechris,Benedikt Löwe,John R. Steel |
Publsiher | : Unknown |
Total Pages | : 552 |
Release | : 2016 |
Genre | : MATHEMATICS |
ISBN | : 1316588084 |
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The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.
Ordinal Definability and Recursion Theory
Author | : Alexander S. Kechris,Benedikt Löwe,John R. Steel |
Publsiher | : Unknown |
Total Pages | : 553 |
Release | : 2015 |
Genre | : Game theory |
ISBN | : 1316587363 |
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The third in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
Recursion Theory
Author | : Chi Tat Chong,Liang Yu |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 320 |
Release | : 2015-08-17 |
Genre | : Mathematics |
ISBN | : 9783110275643 |
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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.
Higher Recursion Theory
Author | : Gerald E. Sacks |
Publsiher | : Cambridge University Press |
Total Pages | : 361 |
Release | : 2017-03-02 |
Genre | : Mathematics |
ISBN | : 9781107168435 |
Download Higher Recursion Theory Book in PDF, Epub and Kindle
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Techniques of Admissible Recursion Theory
Author | : C. T. Chong |
Publsiher | : Springer |
Total Pages | : 223 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 9783540391210 |
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Classical Recursion Theory
Author | : P. Odifreddi |
Publsiher | : Elsevier |
Total Pages | : 667 |
Release | : 1992-02-04 |
Genre | : Computers |
ISBN | : 0080886590 |
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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.
Definability and Computability
Author | : I︠U︡riĭ Leonidovich Ershov |
Publsiher | : Springer Science & Business Media |
Total Pages | : 288 |
Release | : 1996-04-30 |
Genre | : Mathematics |
ISBN | : 0306110393 |
Download Definability and Computability Book in PDF, Epub and Kindle
In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the Gödel incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.