On the length of proofs of finitistic consistency statements in first order theories

Studies in Logic and the Foundations of Mathematics

Volumn 120, Issue C, 1986, Pages 165-196

  Pudlágk, Pavel ^a  

^a MATHEMATICAL INSTITUTE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956963196     PISSN: 0049237X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0049-237X(08)70462-2     Document Type: Article

References (20)

1. J.H. Bennett, On Spectra, P.D. dissertation, Princeton University, 1962.
2. C. Dimitracopoulos, Matijasevič's Theorem and Fragments of Arithmetic, Ph.D. thesis, University of Manchester, (1980).
3. Esenin-Volpin, A.S., The ultraintuitionistic criticism and the antitraditional programme for foundations of mathematics. Kino, A., Myhill, J., Vesley, R.E., (eds.) Intuitionism and Proof Theory, 1970, NHPC, 3–45.
4. Ehrenfencht, A., Mycielski, J., Abbreviating proofs by adding new axioms. Bulletin of the A.M.S. 77 (1971), 366–367.
5. Ferrante, J., Rackoff, Ch.W., The Computational Complexity of Logical Theories, 1979, Springer-Verlag LNM 718.
6. Gandy, R.O., van Dalen, D., Lascar, D., Smiley, T.J., (eds.) Limitations to mathematical knowledge, 1982, NHPC, 129–146 in Logic Colloquium ′80.
7. Gödel, K., Uber die Läge der Beweise. Ergebuisse eines mathematischen Kolloquiums 7 (1936), 23–24 (English translation in.
8. Davis, M., (eds.) The Undecidable, 1965, Raven Press, 82–83.
9. Mendelson, E., Introduction to Mathematical Logic, 1964, D. Van Nostrand Co.
10. Mostowski, A., Sentences Undecidable in Formalized Arithmetic, 1952, NHPC.
11. J. Mycielski, Finitistic intuitions supporting the consistency of ZF and ZF + AD. (manuscript).
12. Parikh, R., Existence and feasibility in arithmetic. J.S.L. 36 (1971), 494–508.
13. Parikh, R., Some results on the lengths of proofs. T.A.M.S. 177 (1973), 29–36.
14. J. Paris and A. Wilkie, On the scheme of induction for bounded formulae, manuscript.
15. P. Pudlák, Cuts, consistency statements and interpretations, to appear in J.S.L.
16. Pudlák, P., Some prime elements in the lattice of interpretability types. T.A.M.S. 280 (1983), 255–275.
17. Statman, R., Bounds for proof-search and speed-up in the predicate calculus. Annals of Math. Logic 15 (1978), 225–287.
18. Statman, R., Speed-up by theories with infinite models. Proceedings of the A.M.S. 81 (1981), 465–469.
19. Vaught, R.L., Axiomatizability by a schema. J.S.L. 32 (1967), 473–479.
20. Yukami, J., Some results on speed-up. The Annals of the Japan Association for Philosophy of Science 6 (1984), 195–205.