Codable sets and orbits of computably enumerable sets

Journal of Symbolic Logic 63 (1):1-28 (1998)
A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has a certain "slowness" property whereby the elements must enter X slowly (under a certain precise complexity measure of speed of computation) even though X may have high information content. Second we prove that every X with this slowness property is computable in some member of any nontrivial orbit, namely for any noncomputable A ∈ ε there exists B in the orbit of A such that X ≤ T B under relative Turing computability (≤ T ). We produce B using the Δ 0 3 -automorphism method we introduced earlier
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2586583
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,861
Through your library
References found in this work BETA
Classes of Recursively Enumerable Sets and Degrees of Unsolvability.Donald A. Martin - 1966 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 12 (1):295-310.

Add more references

Citations of this work BETA
Definable Properties of the Computably Enumerable Sets.Leo Harrington & Robert I. Soare - 1998 - Annals of Pure and Applied Logic 94 (1-3):97-125.
Some Orbits for E.Peter Cholak, Rod Downey & Eberhard Herrmann - 2001 - Annals of Pure and Applied Logic 107 (1-3):193-226.
On N -Tardy Sets.Peter A. Cholak, Peter M. Gerdes & Karen Lange - 2012 - Annals of Pure and Applied Logic 163 (9):1252-1270.

Add more citations

Similar books and articles
Computability Results Used in Differential Geometry.Barbara F. Csima & Robert I. Soare - 2006 - Journal of Symbolic Logic 71 (4):1394 - 1410.
Definable Incompleteness and Friedberg Splittings.Russell Miller - 2002 - Journal of Symbolic Logic 67 (2):679-696.
Recursively Enumerable Generic Sets.Wolfgang Maass - 1982 - Journal of Symbolic Logic 47 (4):809-823.
On the Orbits of Hyperhypersimple Sets.Wolfgang Maass - 1984 - Journal of Symbolic Logic 49 (1):51-62.
On Orbits of Prompt and Low Computably Enumerable Sets.Kevin Wald - 2002 - Journal of Symbolic Logic 67 (2):649-678.
Added to PP index

Total downloads
9 ( #501,829 of 2,210,588 )

Recent downloads (6 months)
2 ( #227,012 of 2,210,588 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature