Definability And Computability
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Definability And Computability
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Author : I︠U︡riĭ Leonidovich Ershov
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-04-30
Definability And Computability written by I︠U︡riĭ Leonidovich Ershov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-04-30 with Mathematics categories.
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.
Definability And Computability
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Author : I͡Uriĭ Leonidovich Ershov
language : en
Publisher:
Release Date : 1996
Definability And Computability written by I͡Uriĭ Leonidovich Ershov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Computable functions categories.
Definability In Arithmetics And Computability
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Author : Université catholique de Louvain (1970- ). Département de philosophie
language : en
Publisher:
Release Date : 2000
Definability In Arithmetics And Computability written by Université catholique de Louvain (1970- ). Département de philosophie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computable functions categories.
Final Report On The Project Definability And Computability Over Finite Structures
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Author : Erich Grädel
language : en
Publisher:
Release Date : 1999
Final Report On The Project Definability And Computability Over Finite Structures written by Erich Grädel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Computability Definability And Algebraic Structures
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Author : Rod Downey
language : en
Publisher:
Release Date : 1999
Computability Definability And Algebraic Structures written by Rod Downey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Computational complexity categories.
Computability Theory
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Author : S. Barry Cooper
language : en
Publisher: CRC Press
Release Date : 2017-09-06
Computability Theory written by S. Barry Cooper and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.
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.
A Hierarchy Of Turing Degrees
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Author : Rod Downey
language : en
Publisher: Princeton University Press
Release Date : 2020-06-16
A Hierarchy Of Turing Degrees written by Rod Downey and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-16 with Mathematics categories.
Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications in topology, group theory, and other subfields. In A Hierarchy of Turing Degrees, Rod Downey and Noam Greenberg introduce a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. Downey and Greenberg present numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers. Blending traditional and modern research results in computability theory, A Hierarchy of Turing Degrees establishes novel directions in the field.
Computability Definability Categoricity And Automorphisms
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Author : Russell Geddes Miller
language : en
Publisher:
Release Date : 2000
Computability Definability Categoricity And Automorphisms written by Russell Geddes Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Automorphisms categories.
Computability And Logic
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Author : George Boolos
language : en
Publisher: CUP Archive
Release Date : 1974-07-18
Computability And Logic written by George Boolos and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-07-18 with Mathematics categories.
Effective Mathematics Of The Uncountable
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Author : Noam Greenberg
language : en
Publisher: Cambridge University Press
Release Date : 2013-10-31
Effective Mathematics Of The Uncountable written by Noam Greenberg 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 2013-10-31 with Mathematics categories.
Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.