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 Title: Partition Theorems and Computability Theory Author(s): Mileti, Joseph Roy Doctoral Committee Chair(s): Jockusch, Carl G., Jr. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics 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. Issue Date: 2004 Type: Text Language: English Description: 76 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004. URI: http://hdl.handle.net/2142/86840 Other Identifier(s): (MiAaPQ)AAI3153383 Date Available in IDEALS: 2015-09-28 Date Deposited: 2004
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