Partition Theorems and Computability Theory

Joseph R. Mileti
2005 Bulletin of Symbolic Logic  
The connections between mathematical logic and combinatorics have a rich history. This paper focuses on one aspect of this relationship: understanding the strength, measured using the tools of computability theory and reverse mathematics, of various partition theorems. To set the stage, recall two of the most fundamental combinatorial principles, König's Lemma and Ramsey's Theorem. We denote the set of natural numbers by ω and the set of finite sequences of natural numbers by ω<ω. We also
more » ... ntify each n ∈ ω with its set of predecessors, so n = {0, 1, 2, ..., n − 1}.
doi:10.2178/bsl/1122038995 fatcat:auevbp5frjgsplkxupnaqpbr6e