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 , 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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