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A short proof of two recently discovered independence results using recursion theoretic methods. (English) Zbl 0512.03028


MSC:

03F35 Second- and higher-order arithmetic and fragments
03D35 Undecidability and degrees of sets of sentences
03D55 Hierarchies of computability and definability
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[1] 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.
[2] Laurie Kirby and Jeff Paris, Accessible independence results for Peano arithmetic, Bull. London Math. Soc. 14 (1982), no. 4, 285 – 293. · Zbl 0501.03017 · doi:10.1112/blms/14.4.285
[3] S. S. Wainer, A classification of the ordinal recursive functions, Arch. Math. Logik Grundlagenforsch. 13 (1970), 136 – 153. · Zbl 0228.02027 · doi:10.1007/BF01973619
[4] S. S. Wainer, Ordinal recursion, and a refinement of the extended Grzegorczyk hierarchy, J. Symbolic Logic 37 (1972), 281 – 292. · Zbl 0261.02031 · doi:10.2307/2272973
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