In the study of cappable and noncappable properties of the recur- sively enumerable (r.e.) degrees, Lempp suggested a conjecture which asserts that for all r.e. degrees a and b, if a≮＝ b then there exists an r. E. degree c such that c ＜＝a and c≮＝b and c is cappable. W e shall prove in this paper that this conjecture holds under the condition that a is high. Working below a high r.e. degree h, we show that for any r.e. degree b with h≮＝b, there exist r.e. degrees a_0 and a_1 such that a_0, a_1≮＝b, a_0, a_1＜＝h, and a_0 and a_1 form a minimal pair.
展开▼
