On definable filters in computably enumerable degrees

Based on a result of Nies on definability the upper semilattice of computably enumerable degrees (denoted by R), we find that in R filters generated by definable subsets are also definable. As applications we demonstrate two new definable filters and study their supremum. Finally we demonstrate a counterexample.

• Type: Journal
• Year: 2007
• Where: APAL
• Authors: Wei Wang, Decheng Ding
• Keywords: APAL 2007, Definable Subsets, Enumerable Degrees, Upper Semilattice