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
C.G. Jockusch, Jr. "Ramsey’s Theorem and Recursion Theory" Journal of Symbolic Logic 37-2 June 1972
L.A. Kirby Ph.D. Thesis Manchester University 1977
L.A. Kirby and J. Paris "Initial Segments of Models of Peano’s Axioms" Lecture Notes in Mathematics 619 Springer Verlag
E. Kleinberg and R. Shore "Square Bracket Partition Relations" Journal of Symbolic Logic 37–4 1972
M. Rabin "Effective Computability of Winning Strategies" Contributions to the Theory of Games 3, Annals of Math. Study 39 Princeton 1957
H. Rogers, Jr. Theory of Recursive Functions and Effective Computability McGraw-Hill 1967
J.R. Shoenfield Degrees of Unsolvability North Holland 1971
J.R. Shoenfield Mathematical Logic Addison-Wesley 1967
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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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