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

Format:

Book

Author/Creator:

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

Greenberg, Noam, 1974- author.

Series:

Annals of mathematics studies ; no. 206.

Annals of mathematics studies ; number 206

Language:

English

Subjects (All):

Unsolvability (Mathematical logic).

Computable functions.

Recursively enumerable sets.

Physical Description:

viii, 222 pages : illustrations ; 24 cm.

Place of Publication:

Princeton, New Jersey : Princeton University Press, 2020.

Summary:

"This book presents new results in computability theory, a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field's connections with disparate areas of mathematical logic and mathematics more generally have grown deeper, and now have a variety of applications in topology, group theory, and other subfields. This monograph establishes new directions in the field, blending classic results with modern research areas such as algorithmic randomness. The significance of the book lies not only in the depth of the results contained therein, but also in the fact that the notions the authors introduce allow them to unify results from several subfields of computability theory"-- Provided by publisher.

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:

Includes bibliographical references (pages [215]-222).

ISBN:

9780691199658

0691199655

9780691199665

0691199663

OCLC:

1145894088