5 papers · 1 filter
Robinson Splitting Theorem and Induction
Yong Liu, Cheng Peng, Mengzhou Sun
The Robinson Splitting Theorem states that a c.e. degree splits over any low c.e. degree . We prove that a weaker version of this theorem holds…
Bi-Isolated d.c.e. Degrees and Induction
Yong Liu, Cheng Peng
A Turing degree is d.c.e. if it contains a set that is the difference of two c.e. sets. A d.c.e. degree is isolated if there exists a c.e. degree $\mathbf{a}<\mathbf{d…
Isolated d.c.e. degrees and induction
Yiqun Liu, Yong Liu, Cheng Peng
A Turing degree is d.c.e. if it contains a set that is the difference of two c.e. sets. A d.c.e. degree is isolated by a c.e. degree if all c.e…
Finite final segments of the d.c.e. Turing degrees
Steffen Lempp, Yiqun Liu, Yong Liu +3
We prove that every finite distributive lattice is isomorphic to a final segment of the d.c.e. Turing degrees (i.e., the degrees of differences of computably enumerable sets). As a…
On the Nonexistence of a Strong Minimal Pair
Mingzhong Cai, Yiqun Liu, Yong Liu +2
Two nonzero recursively enumerable (r.e.) degrees and form a strong minimal pair if and $\mathbf{b}\vee \mathbf{…