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Weak partition relations, finite games, and independence results in Peano arithmetic

Part of the Lecture Notes in Mathematics book series (LNM,volume 834)

Abstract

A basis and an anti-basis result is given for the complexity of infinite weakly homogeneous sets and for winning strategies of finite games. Then using Kirby-Paris indicator theory, we give some independence results for Peano arithmetic.

Except for theorem 1.5 this material appears in my thesis from Duke University 1979. I want to thank most warmly Prof. K. McAloon.

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References

  1. C.G. Jockusch, Jr. "Ramsey’s Theorem and Recursion Theory" Journal of Symbolic Logic 37-2 June 1972

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  2. L.A. Kirby Ph.D. Thesis Manchester University 1977

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© 1980 Springer-Verlag

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Clote, P. (1980). Weak partition relations, finite games, and independence results in Peano arithmetic. In: Pacholski, L., Wierzejewski, J., Wilkie, A.J. (eds) Model Theory of Algebra and Arithmetic. Lecture Notes in Mathematics, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090161

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  • DOI: https://doi.org/10.1007/BFb0090161

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10269-4

  • Online ISBN: 978-3-540-38393-2

  • eBook Packages: Springer Book Archive