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Proceedings of the American Mathematical Society

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A short proof of two recently discovered independence results using recursion theoretic methods


Author: E. A. Cichon
Journal: Proc. Amer. Math. Soc. 87 (1983), 704-706
MSC: Primary 03F30; Secondary 03D20, 10N15
DOI: https://doi.org/10.1090/S0002-9939-1983-0687646-0
MathSciNet review: 687646
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Abstract: Recently L. A. S. Kirby and J. Paris showed that a theorem of R. L. Goodstein cannot be proved in Peano's Arithmetic. We give an alternative short proof of their result, based only on well established results concerning recursion theoretic hierarchies of functions. A second, closely related result, due to F. S. Beckman and K. McAloon, is proved by the same means.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0687646-0
Keywords: Goodstein's theorem, pure number base, cantor normal form, fundamental sequences, slow-growing hierarchy, Hardy hierarchy
Article copyright: © Copyright 1983 American Mathematical Society