A REAL OF STRICTLY POSITIVE EFFECTIVE PACKING DIMENSION THAT DOES NOT COMPUTE A REAL OF EFFECTIVE PACKING DIMENSION ONE

作者：Conidis Chris J^*

来源：Journal of Symbolic Logic, 2012, 77(2): 447-474.

DOI：10.2178/jsl/1333566632

• Computability theory
• Kolmogorov complexity
• effective fractal dimension
• algorithmic randomness

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).

• 出版日期2012-6