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Partition Theorems and Computability Theory

Published online by Cambridge University Press:  15 January 2014

Joseph R. Mileti
Joseph R. Mileti*
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA. E-mail: mileti@math.uchicago.edu
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Extract

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 identify each n ∈ ω with its set of predecessors, so n = {0, 1, 2, …, n − 1}.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 11 , Issue 3 , September 2005 , pp. 411 - 427
Copyright
Copyright © Association for Symbolic Logic 2005

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