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https://hdl.handle.net/2142/86840
Description
Title
Partition Theorems and Computability Theory
Author(s)
Mileti, Joseph Roy
Issue Date
2004
Doctoral Committee Chair(s)
Jockusch, Carl G., Jr.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
"We also study Ramsey degrees, i.e. those Turing degrees which are able to compute homogeneous sets for every computable 2-coloring of pairs of natural numbers, in an attempt to further understand the effective content of Ramsey's Theorem for exponent 2. We establish some new results about these degrees, and obtain as a corollary the nonexistence of a ""universal"" computable 2-coloring of pairs of natural numbers."
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