Dynamic ordinal analysis

Archive for Mathematical Logic

Volumn 42, Issue 4, 2003, Pages 303-334

  Beckmann, Arnold ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

Bounded arithmetic; Cut elimination; Dynamic ordinal; Order induction; Proof theoretic ordinal; Semi formal system

Indexed keywords

EID: 0037526347     PISSN: 09335846     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00153-002-0169-4     Document Type: Article

References (22)

1. Arai, T.: Some results on cut-elimination, provable well-orderings, induction and reflection. Ann. Pure Appl. Logic 95, 93-184 (1998)
2. Baker, T., Gill, J., Solovay, R.: Relativizations of the ℘ = ? script N sign P question. SIAM J. Comput. 4, 431-442 (1975)
3. Beckmann, A.: Seperating fragments of bounded predicative arithmetic. PhD thesis, Westf. Wilhelms-Univ., Münster, 1996.
4. Beckmann, A., Pohlers, W.: Applications of cut-free infinitary derivations to generalized recursion theory. Ann. Pure Appl. Logic 94, 7-19 (1998)
5. Buss, S.R.: Bounded arithmetic, volume 3 of Stud. Proof Theory, Lect. Notes. Bibliopolis, Naples, 1986.
6. Buss, S.R.: Axiomatizations and conservation results for fragments of bounded arithmetic. In Wilfried Sieg, editor, Logic and Computation number 106 in Contemp. Math., p 57-84, Providence, July 1990. Amer. Math. Soc.
7. Buss, S.R.: Relating the bounded arithmetic and the polynomial time hierarchies. Ann. Pure Appl. Logic 75, 67-77 (1995)
8. Clote, P., Krajíček, J.: editors: Arithmetic, proof theory, and computational complexity. Oxford Logic Guides. Oxford University Press, New York, 1993. Papers from the conference held in Prague, July 2-5, 1991, Oxford Science Publications.
9. Håstad, J.: Computational limitations of small-depth circuits. MIT Press, Cambridge, MA 1987.
10. Johannsen, J.: A note on sharply bounded arithmetic. Arch. Math. Logik Grundlag. 33, 159-165 (1994)
11. Krajíček, J.: Fragments of bounded arithmetic and bounded query classes. Trans. Amer. Math. Soc. 338, 587-598 (1993)
12. Krajíček, J.: Bounded Arithmetic, Prepositional Logic, and Comp lexity Theory. Cambridge University Press, Heidelberg/New York, 1995.
13. Krajíček, J., Pudlák, P., Takeuti, G.: Bounded arithmetic and the polynomial hierarchy. Ann. Pure Appl. Logic 52, 143-153 (1991)
14. Parikh, R.J.: Existence and feasibility in arithmetic. J. Symbolic Logic 36, 494-508 (1971)
15. Pohlers, W.: Proof Theory. An Introduction. Number 1407 in Lect. Notes Math. Springer, Berlin/Heidelberg/New York, 1989.
16. Pollett, C.: Structure and definability in general bounded arithmetic theories. Ann. Pure Appl. Logic 100, 189-245 (1999)
17. Schütte, K.: Proof Theory. Number 225 in Grundl. math. Wiss. Springer, Heidelberg/New York, 1977.
18. 0. In Clote and Krajíček [8], p. 320-363. Papers from the conference held in Prague, July 2-5, 1991, Oxford Science Publications.
19. Takeuti, G.: RSUV isomorphism. In Clote and Krajíček [8], p. 364-386. Papers from the conference held in Prague, July 2-5,1991, Oxford Science Publications
20. Wilkie, A.J., Paris, J.B.: On the scheme of induction for bounded arithmetic formulas. Ann. Pure Appl. Logic 35(3), 261-302 (1987)
21. Yao, A.C. Separating the polynomial-time hierarchy by oracles. Proc. 26th Ann. IEEE Symp. on Foundations of Computer Science p. 1-10 (1985)
22. Zambella, D.: Notes on polynomially bounded arithmetic. J. Symbolic Logic 61, 942-966 (1996)