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Reverse mathematics, computability, and partitions of trees

  • Jennifer Chubb (a1), Jeffry L. Hirst (a2) and Timothy H. McNicholl (a3)
Abstract

We examine the reverse mathematics and computability theory of a form of Ramsey's theorem in which the linear n-tuples of a binary tree are colored.

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[1]Cholak, Peter A., Jockusch, Carl G., and Slaman, Theodore A., On the strength of Ramsey's theorem for pairs, this Journal, vol. 66 (2001), no. 1, pp. 155.
[2]Deuber, W., Graham, R. L., Promel, H. J., and Voigt, B., A canonical partition theorem for equivalence relations on Zt, Journal of Combinatorial Theory, Series A, vol. 34 (1983), no. 3, pp. 331339.
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[7]McNicnoll, Timothy H., The inclusion problem for generalized frequency classes, Ph.D. thesis, The George Washington University, 1995.
[8]Milliken, Keith R., A Ramsey theorem for trees, Journal of Combinatorial Theory. Series A, vol. 26 (1979), no. 3, pp. 215237.
[9]Rogers, Hartley Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill Book Co., New York, 1967.
[10]Simpson, Stephen G., Subsystems of Second Order Arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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