A real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one
Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in , where the author constructs a Turing degree of non-integral Hausdorff dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one (on the other hand, it is known via [10, 3, 7] that every real of strictly positive effective Hausdorff dimension computes reals whose effective packing dimensions are arbitrarily close to, but not necessarily equal to, one).
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1333566632
Digital Object Identifier: doi:10.2178/jsl/1333566632
Zentralblatt MATH identifier: 06047771
Mathematical Reviews number (MathSciNet): MR2963016