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Reverse mathematics, computability, and partitions of trees

Published online by Cambridge University Press:  12 March 2014

Jennifer Chubb ,
Jeffry L. Hirst  and
Timothy H. McNicholl
Jennifer Chubb
Affiliation:
The George Washington University, Department of Mathematics, 2115 G Street NW, Washington, Dc 20052, USA, E-mail: jchubb@gwu.edu, URL: http://home.gwu.edu/~jchubb
Jeffry L. Hirst
Affiliation:
Appalachian State University, Department of Mathematical Sciences, Boone, Nc 28608, USA, E-mail: jlh@math.appstate.edu, URL: www.mathsci.appstate.edu/~jlh
Timothy H. McNicholl
Affiliation:
Lamar University, Department of Mathematics, 200 Lucas Building, Beaumont, Tx 77710, USA, E-mail: mcnichollth@my.lamar.eduURL: www.math.lamar.edu/faculty/mcnicholl/mcnicholl.asp
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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.

Keywords

Ramseytreearithmeticalcomprehensionbounds
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 1 , March 2009 , pp. 201 - 215
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

[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. 1–55.Google Scholar
[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. 331–339.CrossRefGoogle Scholar
[3]Hirst, Jeffry L., Combinatorics in subsystems of second order arithmetic, Ph.D. thesis, The Pennsylvania State University, 1987.Google Scholar
[4]Hummel, Tamara Lakins, Effective versions of Ramsey's theorem: Avoiding the cone above 0′, this Journal, vol. 59 (1994), no. 4, pp. 1301–1325.Google Scholar
[5]Jockusch, Carl G. Jr., Ramsey's theorem and recursion theory, this Journal, vol. 37 (1972), pp. 268–280.Google Scholar
[6]Jockusch, Carl G. Jr. and Soare, Robert I., classes and degrees of theories. Transactions of the American Mathematical Society, vol. 173 (1972), pp. 33–56.Google Scholar
[7]McNicnoll, Timothy H., The inclusion problem for generalized frequency classes, Ph.D. thesis, The George Washington University, 1995.Google Scholar
[8]Milliken, Keith R., A Ramsey theorem for trees, Journal of Combinatorial Theory. Series A, vol. 26 (1979), no. 3, pp. 215–237.CrossRefGoogle Scholar
[9]Rogers, Hartley Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill Book Co., New York, 1967.Google Scholar
[10]Simpson, Stephen G., Subsystems of Second Order Arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.CrossRefGoogle Scholar