Turing degrees of reals of positive effective packing dimension

A relatively longstanding question in algorithmic randomness is Jan Reimann's question whether there is a Turing cone of broken dimension. That is, is there a real A such that {B : B T A} contains no 1-random real, yet contains elements of nonzero effective Hausdorff Dimension? We show that the answer is affirmative if Hausdorff dimension is replaced by its inner analogue packing dimension. We construct a minimal degree of effective

• Type: Journal
• Year: 2008
• Where: IPL
• Authors: Rod Downey, Noam Greenberg
• Keywords: Dimension, Hausdorff Dimension, IPL 2008, Longstanding Question