Downey / Greenberg A Hierarchy of Turing Degrees

A Transfinite Hierarchy of Lowness Notions in the Computably Enumerable Degrees, Unifying Classes, and Natural Definability
1. Auflage 2020
ISBN: 978-0-691-20021-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 206, 240 Seiten

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Downey, Rod

Greenberg, Noam

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik EDV | Informatik Informatik

Über Autor(innen)

Rod Downey and Noam Greenberg are professors of mathematics at Victoria University of Wellington in New Zealand. Downey is the coauthor of Parameterized Complexity, Algorithmic Randomness and Complexity, and Fundamentals of Parameterized Complexity. Greenberg is the author of The Role of True Finiteness in the Admissible Recursively Enumerable Degrees.