Splitting and nonsplitting II: A low {\sb 2$} C.E. degree about which ${\bf 0}'$ is not splittable

Journal of Symbolic Logic 67 (4):1391-1430 (2002)
  Copy   BIBTEX

Abstract

It is shown that there exists a low2 Harrington non-splitting base-that is, a low2 computably enumerable (c.e.) degree a such that for any c.e. degrees x, y, if $0' = x \vee y$ , then either $0' = x \vee a$ or $0' = y \vee a$ . Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the $low_{2}-ness$ requirements to be satisfied, and the proof given involves new techniques with potentially wider application

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

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 the distribution of Lachlan nonsplitting bases.S. Barry Cooper, Angsheng Li & Xiaoding Yi - 2002 - Archive for Mathematical Logic 41 (5):455-482.
A Splitting with Infimum in the d-c. e. Degrees.Q. Lei, L. Hong & D. Decheng - 2000 - Mathematical Logic Quarterly 46 (1):53-76.
Bounding Nonsplitting Enumeration Degrees.Thomas F. Kent & Andrea Sorbi - 2007 - Journal of Symbolic Logic 72 (4):1405 - 1417.
Splittings of 0' into the Recursively Enumerable Degrees.Xiaoding Yi - 1996 - Mathematical Logic Quarterly 42 (1):249-269.
There is no low maximal d. c. e. degree– Corrigendum.M. Arslanov & S. B. Cooper - 2004 - Mathematical Logic Quarterly 50 (6):628.
Ray-Splitting Billiards.R. Blümel, P. M. Koch & L. Sirko - 2001 - Foundations of Physics 31 (2):269-281.
Analytic countably splitting families.Otmar Spinas - 2004 - Journal of Symbolic Logic 69 (1):101-117.
On the Universal Splitting Property.Rod Downey - 1997 - Mathematical Logic Quarterly 43 (3):311-320.
Nonsplitting Subset of $mathscr{P}_kappa(kappa^+)$.Moti Gitik - 1985 - Journal of Symbolic Logic 50 (4):881-894.
A splitting theorem for the Medvedev and Muchnik lattices.Stephen Binns - 2003 - Mathematical Logic Quarterly 49 (4):327.
A non-splitting theorem in the enumeration degrees.Mariya Ivanova Soskova - 2009 - Annals of Pure and Applied Logic 160 (3):400-418.

Analytics

Added to PP
2009-01-28

Downloads
94 (#179,190)

6 months
7 (#411,886)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

On Lachlan’s major sub-degree problem.S. Barry Cooper & Angsheng Li - 2008 - Archive for Mathematical Logic 47 (4):341-434.

Add more citations

References found in this work

Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
Working below a low2 recursively enumerably degree.Richard A. Shore & Theodore A. Slaman - 1990 - Archive for Mathematical Logic 29 (3):201-211.
Properly Σ2 Enumeration Degrees.S. B. Cooper & C. S. Copestake - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (6):491-522.
On the distribution of Lachlan nonsplitting bases.S. Barry Cooper, Angsheng Li & Xiaoding Yi - 2002 - Archive for Mathematical Logic 41 (5):455-482.

View all 6 references / Add more references