摘要
In the study of cappable and noncappable properties of the recursively 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. We 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 aO and al such that a0, al ≮ b, aO,a1 ≮ h, and aO and a1 form a minimal pair.
In the study of cappable and noncappable properties of the recursively 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. We 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 aO and al such that a0, al ≮ b, aO,a1 ≮ h, and aO and a1 form a minimal pair.
基金
This reserch is supported by the National Natural Science Foundation of China (No.19971090).
