Partition Theorems and Computability Theory

76 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.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.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD