On Lachlan's major sub-degree problem

The Major Sub-degree Problem of A. H. Lachlan (first posed in 1967) has become a long-standing open question concerning the structure of the computably enumerable (c.e.) degrees. A c.e. degree a is a major subdegree of a c.e. degree b > a if for any c.e. degree x, 0 = b x if and only if 0 = a x. In this paper, we show that every c.e. degree b = 0 or 0 has a major sub-degree, answering Lachlan's question affirmatively.

• Type: Journal
• Year: 2008
• Where: AML
• Authors: S. Barry Cooper, Angsheng Li
• Keywords: AML 2008, Long-standing Open Question, Major Sub-degree Problem, Major Subdegree