Minimal bounds and members of effectively closed sets

We show that there exists a non-empty $\Pi^0_1$ class, with no recursive element, in which no member is a minimal cover for any Turing degree.Comment: 15 pages, 4 figures, 1 acknowledgemen

Computability Theory

Computability is one of the fundamental notions of mathematics, trying to capture the effective content of mathematics. Starting from Gödel’s Incompleteness Theorem, it has now blossomed into a rich area with strong connections with other areas of mathematical logic as well as algebra and theoretical computer science