APAL
2011
12 years 11 months ago
2011
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...
JSYML
2002
13 years 4 months ago
2002
A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many ...
JSYML
2007
13 years 4 months ago
2007
We study the problem of existence of maximal chains in the Turing degrees. We show that:
AML
2006
13 years 4 months ago
2006
We prove that the existential theory of the Turing degrees, in the language with Turing reduction, 0, and unary relations for the classes in the generalized high/low hierarchy, is ...
APAL
2008
13 years 4 months ago
2008
There is a perfect thin 0 1 class whose upward closure in the Turing degrees has full measure (and indeed contains every 2-random degree.) Thus, in the Muchnik lattice of 0 1 class...
APAL
2010
13 years 4 months ago
2010
It is shown that every locally countable upper semi-lattice of cardinality continuum can be embedded into the Turing degrees, assuming Martin's Axiom.
CIE
2009
Springer
13 years 8 months ago
2009
Springer
An algebraic field extension of Q or Z/(p) may be regarded either as a structure in its own right, or as a subfield of its algebraic closure F (either Q or Z/(p)). We consider the ...
CIE
2007
Springer
13 years 10 months ago
2007
Springer
Abstract. We study existence problems of maximal antichains in the Turing degrees. In particular, we give a characterization of the existence of a thin Π1 1 maximal antichains in ...