The K -Degrees, Low for K Degrees,and Weakly Low for K Sets

Notre Dame Journal of Formal Logic 50 (4):381-391 (2009)
Abstract
We call A weakly low for K if there is a c such that $K^A(\sigma)\geq K(\sigma)-c$ for infinitely many σ; in other words, there are infinitely many strings that A does not help compress. We prove that A is weakly low for K if and only if Chaitin's Ω is A-random. This has consequences in the K-degrees and the low for K (i.e., low for random) degrees. Furthermore, we prove that the initial segment prefix-free complexity of 2-random reals is infinitely often maximal. This had previously been proved for plain Kolmogorov complexity
Keywords Martin-Lof randomness   prefix-free Kolmogorov complexity
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,316
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
David Diamondstone (2012). Low Upper Bounds in the LR Degrees. Annals of Pure and Applied Logic 163 (3):314-320.
Similar books and articles
Guohua Wu (2006). Jump Operator and Yates Degrees. Journal of Symbolic Logic 71 (1):252 - 264.
Michael Stob (1983). Wtt-Degrees and T-Degrees of R.E. Sets. Journal of Symbolic Logic 48 (4):921-930.
Su Gao (1994). The Degrees of Conditional Problems. Journal of Symbolic Logic 59 (1):166-181.
Theodore A. Slaman (1986). On the Kleene Degrees of Π11 Sets. Journal of Symbolic Logic 51 (2):352 - 359.
Guohua Wu (2004). Bi-Isolation in the D.C.E. Degrees. Journal of Symbolic Logic 69 (2):409 - 420.
Analytics

Monthly downloads

Sorry, there are not enough data points to plot this chart.

Added to index

2010-09-13

Total downloads

1 ( #402,963 of 1,096,479 )

Recent downloads (6 months)

0

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.