Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees (Memoirs of the American Mathematical Society) - Softcover

Rodney G. Downey (author),

Softcover

ISBN 10: 1470441624 ISBN 13: 9781470441623

Publisher: American Mathematical Society, 2020

Synopsis

Two of the central concepts for the study of degree structures in computability theory are computably enumerable degrees and minimal degrees. For strong notions of reducibility, such as $m$-deducibility or truth table reducibility, it is possible for computably enumerable degrees to be minimal. For weaker notions of reducibility, such as weak truth table reducibility or Turing reducibility, it is not possible to combine these properties in a single degree.

This book considers how minimal weak truth table degrees interact with computably enumerable Turing degrees and obtain three main results. First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $\Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.

About this title

About the Author

Rodney G. Downey, Victoria University of Wellington, New Zealand.

Keng Meng NgNanyang Technological University, Singapore.

Reed Solomon, University of Connecticut, Storrs, CT USA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2020
• Language: English
• ISBN 10: 1470441624
• ISBN 13: 9781470441623
• Binding: Paperback
• Number of pages: 90