The upward closure of a perfect thin class

There is a perfect thin 0 1 class whose upward closure in the Turing degrees has full measure (and indeed contains every 2-random degree.) Thus, in the Muchnik lattice of 0 1 classes, the degree of 2-random reals is comparable with the degree of some perfect thin class. This solves a question of Simpson [16].

• Type: Journal
• Year: 2008
• Where: APAL
• Authors: Rod Downey, Noam Greenberg, Joseph S. Miller
• Keywords: APAL 2008, Perfect, Turing Degrees, Upward Closure