Definable Filters in the Structure of Bounded Turing Reductions

In this article, we show that there exist c.e. bounded Turing degrees a, b such that 0 < a < 0′, and that for any c.e. bounded Turing degree x, b ∨ x = 0′ if and only if x ≥ a. The result gives an unexpected definability theorem in the structure of bounded Turing reducibilities.