Notre Dame Journal of Formal Logic

Controlling Effective Packing Dimension of $\Delta^{0}_{2}$ Degrees

Jonathan Stephenson

Abstract

This paper presents a refinement of a result by Conidis, who proved that there is a real $X$ of effective packing dimension $0\lt \alpha\lt 1$ which cannot compute any real of effective packing dimension $1$. The original construction was carried out below $\emptyset''$, 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 $X\leq_{T}\emptyset'$.

Article information

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

Dates
Accepted: 29 September 2013
First available in Project Euclid: 16 November 2015

https://projecteuclid.org/euclid.ndjfl/1447683389

Digital Object Identifier
doi:10.1215/00294527-3328401

Mathematical Reviews number (MathSciNet)
MR3447726

Zentralblatt MATH identifier
1352.03048

Citation

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. https://projecteuclid.org/euclid.ndjfl/1447683389

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