Codable Sets and Orbits of Computably Enumerable Sets

Codable Sets and Orbits of Computably Enumerable Sets (1995)

by Leo Harrington , Robert I. Soare

Venue:	J. Symbolic Logic
Citations:	11 - 5 self

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Datum	Value	Source
TITLE	Codable Sets and Orbits of Computably Enumerable Sets	user correction - Legacy Corrections
AUTHOR NAME	Leo Harrington	SVM HeaderParse 0.1
AUTHOR AFFIL	and	SVM HeaderParse 0.2
AUTHOR NAME	Robert I. Soare	SVM HeaderParse 0.1
ABSTRACT	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 E denote the structure of the computably enumerable sets under inclusion, E = (fW e g e2! ; `). We previously exhibited a first order E-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 2 E there exists B in the orbit of A such that X T B under relative Turing computability ( T ). We produce B using the \Delta 0 3 -automorphism method we introduced earli...	user correction - Legacy Corrections
YEAR	1995	user correction - Legacy Corrections
VENUE	J. Symbolic Logic	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	0022--4812	INFERENCE
VOLUME	63	INFERENCE
CITATIONS	20 found	ParsCit 1.0