APAL
2011
13 years 5 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 10 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 10 months ago
2007
We study the problem of existence of maximal chains in the Turing degrees. We show that:
AML
2006
13 years 11 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 11 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 11 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
14 years 2 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
14 years 5 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 ...