Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Randomness, Computability, and Density
SIAM Journal on Computing
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Journal of Computer and System Sciences
The method of the yu–ding theorem and its application
Mathematical Structures in Computer Science
Structures of Some Strong Reducibilities
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Analogues of Chaitin's Omega in the computably enumerable sets
Information Processing Letters
Universal computably enumerable sets and initial segment prefix-free complexity
Information and Computation
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The strong weak truth table reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occurs naturally in proofs in classical computability theory as well as in the recent work of Soare, Nabutovsky and Weinberger on applications of computability to differential geometry. Yu and Ding showed that the relevant degree structure restricted to the c.e. reals has no greatest element, and asked for maximal elements. We answer this question for the case of c.e. sets. Using a doubly non-uniform argument we show that there are no maximal elements in the sw degrees of the c.e. sets. We note that the same holds for the Solovay degrees of c.e. sets.