A real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one
Chris J. Conidis
Source: J. Symbolic Logic Volume 77, Issue 2
(2012), 447-474.
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).
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Keywords: Computability theory; Kolmogorov complexity; effective fractal dimension; algorithmic randomness
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