JC
2000
13 years 11 months ago
2000
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...
APAL
2005
13 years 11 months ago
2005
We investigate operators which take a set X to a set relatively computably enumerable in and above X by studying which such sets X can be so mapped into the Turing degree of K. We...
MSCS
2006
13 years 11 months ago
2006
It is shown that for any 2-computably enumerable Turing degree l, any computably enumerable degree a, and any Turing degree s, if l = 0 , l < a, s 0 , and s is c.e. in a, then...
APAL
2010
13 years 11 months ago
2010
We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of ...
BIRTHDAY
2010
Springer
14 years 20 days ago
2010
Springer
In this note we consider the following decision problems. Let be a fixed first-order signature. (i) Given a first-order theory or ground theory T over of Turing degree , a program...
CIE
2005
Springer
14 years 5 months ago
2005
Springer
Let us say that a c.e. operator E is degree invariant on any given Turing degree a if X, Y ∈ a → E(X) ≡T E(Y ). In [4] we construct a c.e. operator E such that ∀X[X <T E...
CIE
2009
Springer
14 years 6 months ago
2009
Springer
This paper studies the Turing degrees of various properties defined for universal numberings, that is, for numberings which list all partial-recursive functions. In particular pro...