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Accessible Segments of the Fast Growing Hierarchy

Published online by Cambridge University Press:  24 March 2017

S. S. Wainer
Affiliation:
University of Leeds
Johann A. Makowsky
Affiliation:
Technion - Israel Institute of Technology, Haifa
Elena V. Ravve
Affiliation:
Technion - Israel Institute of Technology, Haifa
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Logic Colloquium '95 , pp. 339 - 348
Publisher: Cambridge University Press
Print publication year: 2017

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References

(1) Buchholz, W. “An independence result for (Π1 1 – CA) + (BI)”, Annals of Pure and Applied Logic Vol. 23, 1987, 131–155.Google Scholar
(2) Buchholz, W. Cichon, E.A. and Weiermann, A. “A uniform approach to fundamental sequences and subrecursive hierarchies”, Math. Logic Quarterly Vol. 40, 1994, 273–286.Google Scholar
(3) Friedman, H. and Sheard, M. “ Elementary descent recursion and proof theory”, Annals of Pure and Applied Logic Vol. 71, 1995, 1-45.Google Scholar
(4) Heaton, A.J. and Wainer, S.S. “Axioms for subrecursion theories”, in Cooper, S.B. Slaman, T.A. Wainer, S.S. (Eds.) Computability, Enumerability, Unsolvability, LMS Lecture Notes 224, Cambridge Univ. Press 1996, 123-138.
(5) Heaton, A.J. “A jump operator for subrecursion theory”, in preparation.
(6)Kadota, N. “On Wainer's notation for a minimal subrecursive inaccessible ordinal”, Math. Logic Quarterly Vol. 39, 1993, 217-227.Google Scholar
(7)Kleene, S.C. “Extension of an effectively generated class of functions by enumeration”, Colloquium Mathematicum Vol. 6, 1958, 67-78.Google Scholar
(8)Wainer, S.S. “Slow growing versus fast growing”, Journal of Symbolic Logic Vol. 54, 1989, 608-614.Google Scholar
(9) Wainer, S.S. “Hierarchies of provably computable functions”, in Petkov, P. (Ed.) Mathematical Logic, Plenum Press 1990, 211-220.
(10) Wainer, S.S. “The hierarchy of terminating recursive programs over N” , in Leivant, D. (Ed.), Logic and Computational Complexity, Springer Lecture Notes in Computer Science 960, 1995, 281-299.Google Scholar

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