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» On the Turing Degrees of Divergence Bounded Computable Reals
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CIE
2005
Springer
13 years 11 months ago
On the Turing Degrees of Divergence Bounded Computable Reals
The d-c.e. (difference of c.e.) and dbc (divergence bounded computable) reals are two important subclasses of ∆0 2-reals which have very interesting computability-theoretical as...
Robert Rettinger, Xizhong Zheng
APAL
2011
13 years 11 days ago
Upper bounds on ideals in the computably enumerable Turing degrees
We study ideals in the computably enumerable Turing degrees, and their upper bounds. Every proper Σ0 4 ideal in the c.e. Turing degrees has an incomplete upper bound. It follows t...
George Barmpalias, André Nies
APAL
2010
125views more  APAL 2010»
13 years 5 months ago
The computable Lipschitz degrees of computably enumerable sets are not dense
The computable Lipschitz reducibility was introduced by Downey, Hirschfeldt and LaForte under the name of strong weak truthtable reducibility [6]. This reducibility measures both t...
Adam R. Day
APAL
2006
123views more  APAL 2006»
13 years 5 months ago
The ibT degrees of computably enumerable sets are not dense
Abstract. We show that the identity bounded Turing degrees of computably enumerable sets are not dense.
George Barmpalias, Andrew E. M. Lewis
JC
2000
89views more  JC 2000»
13 years 5 months ago
Weakly Computable Real Numbers
The Turing degree of a real number x is defined as the Turing degree of its binary expansion. This definition is quite natural and robust. In this paper we discuss some basic degr...
Klaus Ambos-Spies, Klaus Weihrauch, Xizhong Zheng