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APAL

2011

8 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

8 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

8 years 10 months ago
2007

We study the problem of existence of maximal chains in the Turing degrees. We show that:

AML

2006

8 years 10 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

8 years 10 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

8 years 10 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

9 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

9 years 4 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 ...