On the r.e. predecessors of d.r.e. degrees

Archive for Mathematical Logic 38 (6):373-386 (1999)
  Copy   BIBTEX

Abstract

Let d be a Turing degree containing differences of recursively enumerable sets (d.r.e.sets) and R[d] be the class of less than d r.e. degrees in whichd is relatively enumerable (r.e.). A.H.Lachlan proved that for any non-recursive d.r.e. d R[d] is not empty. We show that the r.e. degree defined by Lachlan for a d.r.e.set $D\in$ d is just the minimum degree in which D is r.e. Then we study for a given d.r.e. degree d class R[d] and show that there exists a d.r.e.d such that R d] has a minimum element $>$ 0. The most striking result of the paper is the existence of d.r.e. degrees for which R[d] consists of one element. Finally we prove that for some d.r.e. d R[d] can be the interval [a,b] for some r.e. degrees a,b, a $<$ b $<$ d

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 101,693

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On relative enumerability of Turing degrees.Shamil Ishmukhametov - 2000 - Archive for Mathematical Logic 39 (3):145-154.
On a problem of Ishmukhametov.Chengling Fang, Guohua Wu & Mars Yamaleev - 2013 - Archive for Mathematical Logic 52 (7-8):733-741.
An almost-universal cupping degree.Jiang Liu & Guohua Wu - 2011 - Journal of Symbolic Logic 76 (4):1137-1152.
Infima in the d.r.e. degrees.D. Kaddah - 1993 - Annals of Pure and Applied Logic 62 (3):207-263.
Infima of d.r.e. degrees.Jiang Liu, Shenling Wang & Guohua Wu - 2010 - Archive for Mathematical Logic 49 (1):35-49.
On Transfinite Levels of the Ershov Hierarchy.Cheng Peng - 2021 - Bulletin of Symbolic Logic 27 (2):220-221.

Analytics

Added to PP
2013-11-23

Downloads
50 (#445,273)

6 months
10 (#447,160)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Isolation and the high/low hierarchy.Shamil Ishmukhametov & Guohua Wu - 2002 - Archive for Mathematical Logic 41 (3):259-266.
On a problem of Ishmukhametov.Chengling Fang, Guohua Wu & Mars Yamaleev - 2013 - Archive for Mathematical Logic 52 (7-8):733-741.
On relative enumerability of Turing degrees.Shamil Ishmukhametov - 2000 - Archive for Mathematical Logic 39 (3):145-154.

Add more citations

References found in this work

Limiting recursion.E. Mark Gold - 1965 - Journal of Symbolic Logic 30 (1):28-48.
The Isolated D. R. E. Degrees are Dense in the R. E. Degrees.Geoffrey Laforte - 1996 - Mathematical Logic Quarterly 42 (1):83-103.

Add more references