Notre Dame Journal of Formal Logic

Controlling Effective Packing Dimension of Δ20 Degrees

Jonathan Stephenson

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This paper presents a refinement of a result by Conidis, who proved that there is a real X of effective packing dimension 0<α<1 which cannot compute any real of effective packing dimension 1. The original construction was carried out below '', and this paper’s result is an improvement in the effectiveness of the argument, constructing such an X by a limit-computable approximation to get XT'.

Article information

Notre Dame J. Formal Logic, Volume 57, Number 1 (2016), 73-93.

Received: 23 February 2013
Accepted: 29 September 2013
First available in Project Euclid: 16 November 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]
Secondary: 68Q30: Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32]

effective packing dimension limit-computable approximation complexity pruned clumpy trees


Stephenson, Jonathan. Controlling Effective Packing Dimension of $\Delta^{0}_{2}$ Degrees. Notre Dame J. Formal Logic 57 (2016), no. 1, 73--93. doi:10.1215/00294527-3328401.

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