Weakly semirecursive sets

Journal of Symbolic Logic 55 (2):637-644 (1990)
We introduce the notion of "semi-r.e." for subsets of ω, a generalization of "semirecursive" and of "r.e.", and the notion of "weakly semirecursive", a generalization of "semi-r.e.". We show that A is weakly semirecursive iff, for any n numbers x 1 ,...,x n , knowing how many of these numbers belong to A is equivalent to knowing which of these numbers belong to A. It is shown that there exist weakly semirecursive sets that are neither semi-r.e. nor co-semi-r.e. On the other hand, we exhibit nonzero Turing degrees in which every weakly semirecursive set is semirecursive. We characterize the notion "A is weakly semirecursive and recursive in K" in terms of recursive approximations to A. We also show that if a finite Boolean combination of r.e. sets is semirecursive then it must be r.e. or co-r.e. Several open questions are raised
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2274653
 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
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,165
Through your library
References found in this work BETA
Nondeterministic Bounded Query Reducibilities.Richard Beigel, William Gasarch & Jim Owings - 1989 - Annals of Pure and Applied Logic 41 (2):107-118.

Add more references

Citations of this work BETA
Weakly Semirecursive Sets and R.E. Orderings.Martin Kummer & Frank Stephan - 1993 - Annals of Pure and Applied Logic 60 (2):133-150.

Add more citations

Similar books and articles
Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
Located Sets and Reverse Mathematics.Mariagnese Giusto & Stephen G. Simpson - 2000 - Journal of Symbolic Logic 65 (3):1451-1480.
Weakly o-Minimal Structures and Some of Their Properties.B. Sh Kulpeshov - 1998 - Journal of Symbolic Logic 63 (4):1511-1528.
The Classification of Small Weakly Minimal Sets. II.Steven Buechler - 1988 - Journal of Symbolic Logic 53 (2):625-635.
On the Weak Kleene Scheme in Kripke's Theory of Truth.James Cain & Zlatan Damnjanovic - 1991 - Journal of Symbolic Logic 56 (4):1452-1468.
Abstract Logic and Set Theory. II. Large Cardinals.Jouko Väänänen - 1982 - Journal of Symbolic Logic 47 (2):335-346.
On the Structures Inside Truth-Table Degrees.Frank Stephan - 2001 - Journal of Symbolic Logic 66 (2):731-770.

Monthly downloads

Added to index


Total downloads

11 ( #404,708 of 2,172,021 )

Recent downloads (6 months)

1 ( #325,967 of 2,172,021 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums