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A Short Proof of Two Recently Discovered Independence Results Using Recursion Theoretic Methods
E. A. Cichon
Proceedings of the American Mathematical Society
Vol. 87, No. 4 (Apr., 1983), pp. 704-706
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2043364
Page Count: 3
You can always find the topics here!Topics: Mathematical theorems, Recursion, Peano axioms, Mathematical functions, Mathematical induction, Mathematical sequences
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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.
Proceedings of the American Mathematical Society © 1983 American Mathematical Society