Minimal weak truth table degrees and computably enumerable Turing degrees / Rodney G. Downey, Keng Meng Ng, Reed Solomon.

Format:

Book

Author/Creator:

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

Ng, Keng Meng, author.

Solomon, Reed, author.

Series:

Memoirs of the American Mathematical Society ; no. 1284.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1284

Language:

English

Subjects (All):

Unsolvability (Mathematical logic).

Recursively enumerable sets.

Computable functions.

Physical Description:

vii, 90 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2020.

Summary:

"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. We consider 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 Δ02 set which Turing bounds a promptly simple set can have minimal weak truth table degree."--Page vii, abstract.

Contents:

Informal construction

Formal construction

Limiting results.

Notes:

"May 2020, volume 265, number 1284 (first of 7 numbers)."

Includes bibliographical references.

Other Format:

Online version: Downey, Rodney G. Minimal weak truth table degrees and computably enumerable Turing degrees

ISBN:

9781470441623

1470441624

OCLC:

1151804097