A Hierarchy of Turing Degrees

A Hierarchy of Turing Degrees

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.

GET EBOOK

Author
Publisher Princeton University Press
Release Date
ISBN 0691200211
Pages 240 pages
Rating 4/5 (17 users)

More Books:

A Hierarchy of Turing Degrees
Language: en
Pages: 240
Authors: Rod Downey
Categories: Mathematics
Type: BOOK - Published: 2020-06-16 - Publisher: Princeton University Press

Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growi
A Hierarchy of Turing Degrees
Language: en
Pages: 240
Authors: Rod Downey
Categories: Computers
Type: BOOK - Published: 2020-06-16 - Publisher: Princeton University Press

"This book presents new results in computability theory, a branch of mathematical logic and computer science that has become increasingly relevant in recent yea
Turing Computability
Language: en
Pages: 263
Authors: Robert I. Soare
Categories: Computers
Type: BOOK - Published: 2016-06-20 - Publisher: Springer

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 a
Worldviews, Science and Us
Language: en
Pages: 351
Authors: Carlos Gershenson
Categories: Complexity (Philosophy)
Type: BOOK - Published: 2007 - Publisher: World Scientific

Scientific, technological, and cultural changes have always had an impact upon philosophy. They can force a change in the way we perceive the world, reveal new
Proceedings of the 10th Asian Logic Conference, Kobe, Japan, 1-6 September 2008
Language: en
Pages: 393
Authors: Toshiyasu Arai
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: World Scientific

The 10th Asian Logic Conference is part of the series of logic conferences inaugurated in Singapore in 1981. This meeting is held every three years and rotates
Proceedings of the 10th Asian Logic Conference
Language: en
Pages:
Authors:
Categories:
Type: BOOK - Published: - Publisher:

The Foundations of Computability Theory
Language: en
Pages: 422
Authors: Borut Robič
Categories: Computers
Type: BOOK - Published: 2020-11-13 - Publisher: Springer Nature

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical conte
Higher Recursion Theory
Language: en
Pages:
Authors: Gerald E. Sacks
Categories: Mathematics
Type: BOOK - Published: 2017-03-02 - Publisher: Cambridge University Press

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
Computable Structures and the Hyperarithmetical Hierarchy
Language: en
Pages: 366
Authors: C.J. Ash
Categories: Mathematics
Type: BOOK - Published: 2000-06-16 - Publisher: Elsevier

This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity whic
Recursion Theory
Language: en
Pages: 528
Authors: Anil Nerode
Categories: Mathematics
Type: BOOK - Published: 1985 - Publisher: American Mathematical Soc.