The Turing degree $\mathbf{0}'$ is defined as all languages Turing-equivalent to the halting problem.In fact any recursively enumerable language is polynomial-time reducible to the halting problem.My question is, are all languages with Turing degree $\mathbf{0}'$ Turing-reducible to each other in polynomial time?If not, can the fastest reduction between two $\mathbf{0}'$ languages get arbitrarily slow, andare there known subsets of $\mathbf{0}'$ that are polynomial-time reducible to each other?
Polynomial-time reductions between undecidable languages
computability;reductions;polynomial time;halting problem;undecidability