A real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one

Journal of Symbolic Logic 77 (2):447-474 (2012)
Abstract
Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], 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)
Keywords Computability theory   Kolmogorov complexity   effective fractal dimension   algorithmic randomness
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