Every nonzero c . e . strongly bounded Turing degree has the anti - cupping property ∗
نویسندگان
چکیده
The strongly bounded Turing reducibilities r = cl (computable Lipschitz reducibility) and r = ibT (identity bounded Turing reducibility) are defined in terms of Turing reductions where the use function is bounded by the identity function up to an additive constant and the identity function, respectively. We show that, for r = ibT, cl, every computably enumerable (c.e.) r-degree a > 0 has the anti-cupping property in the partial ordering (Rr,≤) of the c.e. r-degrees. The proof is based on (1) the (new) result, that, for any noncomputable c.e. set A there is a noncomputable c.e. set B such that B ≤ibT C for all c.e. sets C with A ≤wtt C and (2) some (old) observations on computable shifts.
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