A short proof of two recently discovered independence results using recursion theoretic methods
HTML articles powered by AMS MathViewer
- by E. A. Cichon PDF
- Proc. Amer. Math. Soc. 87 (1983), 704-706 Request permission
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.References
-
F. S. Beckman and K. Mc Aloon, A direct proof of a result of Goodstein-Kirby-Paris, Lecture Notes, AMS Summer Institute on Recursion Theory, Cornell Univ., Ithaca, N. Y., June 28-July 16, 1982.
- Laurie Kirby and Jeff Paris, Accessible independence results for Peano arithmetic, Bull. London Math. Soc. 14 (1982), no. 4, 285–293. MR 663480, DOI 10.1112/blms/14.4.285
- S. S. Wainer, A classification of the ordinal recursive functions, Arch. Math. Logik Grundlag. 13 (1970), 136–153. MR 294134, DOI 10.1007/BF01973619
- S. S. Wainer, Ordinal recursion, and a refinement of the extended Grzegorczyk hierarchy, J. Symbolic Logic 37 (1972), 281–292. MR 321715, DOI 10.2307/2272973
Additional Information
- © Copyright 1983 American Mathematical Society
- 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