The jump operator on the ω-enumeration degrees

Annals of Pure and Applied Logic 160 (3):289-301 (2009)

The jump operator on the ω-enumeration degrees was introduced in [I.N. Soskov, The ω-enumeration degrees, J. Logic Computat. 17 1193–1214]. In the present paper we prove a jump inversion theorem which allows us to show that the enumeration degrees are first order definable in the structure of the ω-enumeration degrees augmented by the jump operator. Further on we show that the groups of the automorphisms of and of the enumeration degrees are isomorphic. In the second part of the paper we study the jumps of the ω-enumeration degrees below . We define the ideal of the almost zero degrees and obtain a natural characterization of the class H of the ω-enumeration degrees below which are high n for some n and of the class L of the ω-enumeration degrees below which are low n for some n
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2009.01.003
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 43,044
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Then-Rea Enumeration Degrees Are Dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
Jumps of Quasi-Minimal Enumeration Degrees.Kevin McEvoy - 1985 - Journal of Symbolic Logic 50 (3):839-848.
Definability of the Jump Operator in the Enumeration Degrees.I. Sh Kalimullin - 2003 - Journal of Mathematical Logic 3 (02):257-267.

View all 8 references / Add more references

Citations of this work BETA

The Automorphism Group of the Enumeration Degrees.Mariya I. Soskova - 2016 - Annals of Pure and Applied Logic 167 (10):982-999.
The Ω-Turing Degrees.Andrey C. Sariev & Hristo Ganchev - 2014 - Annals of Pure and Applied Logic 165 (9):1512-1532.

Add more citations

Similar books and articles

A Jump Inversion Theorem for the Enumeration Jump.I. N. Soskov - 2000 - Archive for Mathematical Logic 39 (6):417-437.
The Jump Operation for Structure Degrees.V. Baleva - 2006 - Archive for Mathematical Logic 45 (3):249-265.
On the Symmetric Enumeration Degrees.Charles M. Harris - 2007 - Notre Dame Journal of Formal Logic 48 (2):175-204.
Badness and Jump Inversion in the Enumeration Degrees.Charles M. Harris - 2012 - Archive for Mathematical Logic 51 (3-4):373-406.
Limit Lemmas and Jump Inversion in the Enumeration Degrees.Evan J. Griffiths - 2003 - Archive for Mathematical Logic 42 (6):553-562.
On the Jump Classes of Noncuppable Enumeration Degrees.Charles M. Harris - 2011 - Journal of Symbolic Logic 76 (1):177 - 197.
Goodness in the Enumeration and Singleton Degrees.Charles M. Harris - 2010 - Archive for Mathematical Logic 49 (6):673-691.
A Jump Operator on Honest Subrecursive Degrees.Lars Kristiansen - 1998 - Archive for Mathematical Logic 37 (2):105-125.
Noncappable Enumeration Degrees Below 0'e. [REVIEW]S. Barry Cooper & Andrea Sorbi - 1996 - Journal of Symbolic Logic 61 (4):1347 - 1363.
Isolation and the Jump Operator.Guohua Wu - 2001 - Mathematical Logic Quarterly 47 (4):525-534.
Jump Operator and Yates Degrees.Guohua Wu - 2006 - Journal of Symbolic Logic 71 (1):252 - 264.


Added to PP index

Total views
3 ( #1,170,232 of 2,260,165 )

Recent downloads (6 months)
1 ( #905,492 of 2,260,165 )

How can I increase my downloads?


My notes

Sign in to use this feature