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  • Print publication year: 2005
  • Online publication date: March 2017

Provable recursiveness and complexity

[1] S., Bellantoni and S., Cook, A new recursion theoretic characterization of the polytime functions,Computational Complexity, vol. 2 (1992), pp. 97–110.
[2] W., Buchholz, An independence result for Π11 - CA + BI, Annals of Pure and Applied Logic, vol. 23 (1987), pp. 131–155.
[3] W., Burr, Fragments of Heyting arithmetic,The Journal of Symbolic Logic, vol. 65 (2000), pp. 1223–1240.
[4] N., Cagman, G. E., Ostrin, and S. S., Wainer, Proof theoretic complexity of low subrecursive classes,Foundations of secure computation (F. L., Bauer and R., Steinbr öggen, editors), IOS Press, 2000, pp. 249–285.
[5] M., Fairtlough and S. S., Wainer, Hierarchies of provably recursive functions,Handbook of proof theory (S., Buss, editor), Elsevier Science BV, 1998, pp. 149–207.
[6] G., Kreisel, On the interpretation of non-finitist proofs, parts I, II,The Journal of Symbolic Logic, vol. 16 (1951), pp. 241–267, vol. 17 (1952) pp. 43–58.
[7] D., Leivant, A foundational delineation of poly-time,Information and Computation, vol. 110 (1994), pp. 391–420.
[8] D., Leivant, Intrinsic theories and computational complexity,Logic and computational complexity (D., Leivant, editor), Lecture Notes in Computer Science, vol. 960, Springer-Verlag, 1995, pp. 177–194.
[9] J-Y., Marion, Actual arithmetic and feasibility,Proceedings of CSL 2001 (L., Fribourg, editor), Lecture Notes in Computer Science, vol. 2142, Springer-Verlag, 2001, pp. 115–129.
[10] G. E., Ostrin, Proof theories of low subrecursive classes,Ph.D. thesis, Leeds, 1999.
[11] G. E., Ostrin and S. S., Wainer, Elementary arithmetic, Leeds, preprint, 2001, to appear in Annals of Pure and Applied Logic.
[12] D., Rödding, Klassen rekursiver Funktionen,Proceedings of Summer School in Logic, Leeds 1967 (M. H., Löb, editor), Lecture Notes in Mathematics, vol. 70, Springer-Verlag, 1968, pp. 159–222.
[13] A. S., Troelstra and H., Schwichtenberg, Basic proof theory, Cambridge Tracts in Theoretical Computer Science, vol. 43, CUP, 1996.
[14] A., Weiermann, How to characterize provably total functions by local predicativity,The Journal of Symbolic Logic, vol. 61 (1996), pp. 52–69.