Paper Info
Title
A generic set that does not bound a minimal pair
Abstract
The structure of the semi lattice of enumeration degrees has been investigated from many aspects. One aspect is the bounding and nonbounding properties of generic degrees. Copestake proved that every 2-generic enumeration degree bounds a minimal pair and conjectured that there exists a 1-generic set that does not bound a minimal pair. In this paper we verify this longstanding conjecture by constructing such a set using an infinite injury priority argument. The construction is explained in detail. It makes use of a priority tree of strategies.
Year
DOI
Venue
2006
10.1007/11750321_71
TAMC
Keywords
Field
DocType
longstanding conjecture,2-generic enumeration degree,semi lattice,infinite injury priority argument,nonbounding property,generic degree,minimal pair,priority tree,1-generic set,enumeration degree
Discrete mathematics,Minimal pair,Combinatorics,Lattice (order),Existential quantification,Enumeration,Conjecture,Mathematics,Bounding overwatch
Conference
Volume
ISSN
ISBN
3959
0302-9743
3-540-34021-1
Citations 
PageRank 
References 
0
0.34
2
Authors
1
Name
Order
Citations
PageRank
Mariya Ivanova Soskova12110.54