Thin Maximal Antichains in the Turing Degrees

Abstract. We study existence problems of maximal antichains in the Turing degrees. In particular, we give a characterization of the existence of a thin Π1 1 maximal antichains in the Turing degrees in terms of (relatively) constructible reals. A corollary of our main result gives a negative solution to a question of Jockusch under the assumption that every real is constructible.

• Type: Conference
• Year: 2007
• Where: CIE
• Authors: Chi Tat Chong, Liang Yu
• Keywords: CIE 2007, Existence Problems, Maximal Antichains, Turing Degrees