To illustrate the technique, we first reprove Cooper's minimal pair theorem by mixing our procedure with the standard tree proof of the existence of a minimal.
there is a minimal pair of high recursively enumerable degrees a0 and aj below h. We next move up a step to put one of the simplest 0(3) arguments below an.
Ultimately, one would like to find some degree-theoretic properties definable in terms of the ordering of Turing reducibility and quantifiers over the ...
Working below a high recursively enumerable degree. Authors: Richard A. Shore,. T. A. Slaman. Print Book, English, [1990].
... Working below a high recursively enumerable degree (1990). Shore, R.A., Slaman, T.: Splitting and density cannot be combined below any high r.e. degree (1991).
We prove below two theorems related to this. Theorem 1 confirms the conjecture in the restricted case that b is low, with m O b = a replaced by m l b.
Working below a high recursively enumerable degree, Journal of Symbolic Logic 58 (1993), 824-859 (with T. Slaman). Degrees of constructibility, in Set ...
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Minimal degrees of unsolvability and the full approximation construction. Mem. Am. Math. Soc., 162 (1975). Google Scholar. [3]. R.L. Epstein.
We consider the set of jumps below a Turing degree, given by. JB.a/ D ¹x0 W x aº, with a focus on the problem: Which recursively enu-.
This result, though, can be deduced from earlier work. Jockusch ([6]) showed that every 1-generic degree is recursively enumerable in a strictly lower degree.