Avoiding uniformity in theΔ20enumeration degrees

Annals of Pure and Applied Logic 165 (9):1355-1379 (2014)

Abstract
Defining a class of sets to be uniform Δ02 if it is derived from a binary {0,1}{0,1}-valued function f≤TKf≤TK, we show that, for any C⊆DeC⊆De induced by such a class, there exists a high Δ02 degree c which is incomparable with every degree b ϵ Ce \ {0e, 0'e}. We show how this result can be applied to quite general subclasses of the Ershov Hierarchy and we also prove, as a direct corollary, that every nonzero low degree caps with both a high and a nonzero low Δ02 degree
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2014.04.008
Options
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: 42,993
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.
Goodness in the Enumeration and Singleton Degrees.Charles M. Harris - 2010 - Archive for Mathematical Logic 49 (6):673-691.
Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5 (7-13):117-125.
On Minimal Pairs of Enumeration Degrees.Kevin McEvoy & S. Barry Cooper - 1985 - Journal of Symbolic Logic 50 (4):983-1001.

View all 12 references / Add more references

Citations of this work BETA

Initial Segments of the Enumeration Degrees.Hristo Ganchev & Andrea Sorbi - 2016 - Journal of Symbolic Logic 81 (1):316-325.

Add more citations

Similar books and articles

The Jump Operator on the Ω-Enumeration Degrees.Hristo Ganchev & Ivan N. Soskov - 2009 - Annals of Pure and Applied Logic 160 (3):289-301.
A Non-Splitting Theorem in the Enumeration Degrees.Mariya Ivanova Soskova - 2009 - Annals of Pure and Applied Logic 160 (3):400-418.
On the Symmetric Enumeration Degrees.Charles M. Harris - 2007 - Notre Dame Journal of Formal Logic 48 (2):175-204.
Limit Lemmas and Jump Inversion in the Enumeration Degrees.Evan J. Griffiths - 2003 - Archive for Mathematical Logic 42 (6):553-562.
Sets of Generators and Automorphism Bases for the Enumeration Degrees.Andrea Sorbi - 1998 - Annals of Pure and Applied Logic 94 (1-3):263-272.
Goodness in the Enumeration and Singleton Degrees.Charles M. Harris - 2010 - Archive for Mathematical Logic 49 (6):673-691.
The Π₃-Theory of the [Image] -Enumeration Degrees Is Undecidable.Thomas F. Kent - 2006 - Journal of Symbolic Logic 71 (4):1284 - 1302.
Structural Properties and $\Sigma^0_2$ Enumeration Degrees.Andre Nies & Andrea Sorbi - 2000 - Journal of Symbolic Logic 65 (1):285-292.
On the Jump Classes of Noncuppable Enumeration Degrees.Charles M. Harris - 2011 - Journal of Symbolic Logic 76 (1):177 - 197.
Badness and Jump Inversion in the Enumeration Degrees.Charles M. Harris - 2012 - Archive for Mathematical Logic 51 (3-4):373-406.

Analytics

Added to PP index
2015-01-22

Total views
8 ( #816,000 of 2,259,693 )

Recent downloads (6 months)
3 ( #500,092 of 2,259,693 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature