A hierarchy of Turing degrees : a transfinite hierarchy of lowness notions in the computably enumerable degrees, unifying classes, and natural definability / Rod Downey and Noam Greenberg.

Format:

Book

Author/Creator:

Downey, R. G. (Rod G.), author.

Greenberg, Noam, 1974- author.

Series:

Annals of mathematics studies ; number 206.

Princeton scholarship online.

Annals of mathematics studies ; number 206

Princeton scholarship online

Language:

English

Subjects (All):

Unsolvability (Mathematical logic).

Computable functions.

Recursively enumerable sets.

Physical Description:

1 online resource (235 pages) : illustrations.

Place of Publication:

Princeton : Princeton University Press, 2021.

Summary:

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. This book introduces 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. The book presents numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers.

Contents:

[alpha]-c.a. functions

The hierarchy of totally [alpha]-c.a. degrees

Maximal totally [alpha]-c.a. degrees

Presentations of left-c.e. reals

m-topped degrees

Embeddings of the 1-3-1 lattice

Prompt permissions.

Notes:

Previously issued in print: 2020.

Includes bibliographical references.

Description based on online resource; title from home page (viewed on December 17, 2020).

ISBN:

9780691200217

0691200211

OCLC:

1196361575