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APAL
2011
8 years 5 months 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
JSYML
2002
84views more  JSYML 2002»
8 years 10 months ago
Maximal Contiguous Degrees
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 ...
Peter Cholak, Rodney G. Downey, Stephen Walk
JSYML
2007
52views more  JSYML 2007»
8 years 10 months ago
Maximal chains in the Turing degrees
We study the problem of existence of maximal chains in the Turing degrees. We show that:
Chi Tat Chong, Liang Yu
AML
2006
76views more  AML 2006»
8 years 10 months ago
There is no ordering on the classes in the generalized high/low hierarchies
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 ...
Antonio Montalbán
APAL
2008
62views more  APAL 2008»
8 years 10 months ago
The upward closure of a perfect thin class
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...
Rod Downey, Noam Greenberg, Joseph S. Miller
APAL
2010
79views more  APAL 2010»
8 years 10 months ago
Martin's Axiom and embeddings of upper semi-lattices into the Turing degrees
It is shown that every locally countable upper semi-lattice of cardinality continuum can be embedded into the Turing degrees, assuming Martin's Axiom.
Wang Wei
CIE
2009
Springer
9 years 2 months ago
Spectra of Algebraic Fields and Subfields
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 ...
Andrey Frolov, Iskander Sh. Kalimullin, Russell Mi...
CIE
2007
Springer
9 years 4 months ago
Thin Maximal Antichains in the Turing Degrees
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 ...
Chi Tat Chong, Liang Yu
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