Predicative logic and formal arithmetic

Notre Dame Journal of Formal Logic

Volumn 39, Issue 1, 1998, Pages 1-17

  Burgess, John P ^a   Hazen, A P ^b  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85010807045     PISSN: 00294527     EISSN: 19390726     Source Type: Journal    
DOI: 10.1305/ndjfl/1039293018     Document Type: Article

References (22)

1. Bezboruah, A., and J. Shepherdson,“Gödel’s second incompleteness theorem for Q,” The Journal of Symbolic Logic, vol. 41 (1977), pp. 503-12.
2. Feferman, S., “Systems of predicative analysis,” The Journal of Symbolic Logic, vol. 29 (1964), pp. 1-30.
3. Feferman, S., and G. Hellman,“Predicative foundations of arithmetic,” Journal of Philosophical Logic, vol. 24 (1995), pp. 1-17.
4. Grzegorczyk, A., Some Classes of Recursive Functions, Mathematical Reports 4, Mathematical Institute of the Polish Academy of Sciences, Warsaw, 1953.
5. Hájek, P., and P. Pudlák, Metamathematics of First-Order Arithmetic, Perspectives in Mathematical Logic, Springer, Berlin, 1991.
6. Hazen, A. P., “Russellian predicative arithmetic I: Capturing IDO,” Philosophy Preprint Series 2/88, University of Melbourne, 1988.
7. Hazen, A. P., “Interpretability of Robinson arithmetic in the ramified second-order theory of dense linear order,” Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 101-11.
8. Heck, R. G., Jnr., “Grundgesetze der Arithmetik I §§29-32,” Notre Dame Journal of Formal Logic, vol. 38, pp. 437-74.
9. Kalmar, L.,“On unsolvable mathematical problems,” pp. 756-58 in Proceedings of the Tenth International Congress of Philosophy, North-Holland, Amsterdam, 1949.
10. Leivant, D.,“Abstraction and computational complexity” (abstract), The Journal of Symbolic Logic, vol. 55 (1990), pp. 379-80.
11. Leivant, D.,“Finitely stratified polymorphism,” Information and Computing, vol. 93 (1991), pp. 93-113.
12. Montagna, F., and A. Mancini, “A minimal predicative set theory,” Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 186-203.
13. Nelson, E., Predicative Arithmetic, Princeton University Press, Princeton, 1986.
14. Novak Gal, I. L., “A construction of models of consistent systems,” Fundamenta Math-ematicae, vol. 37 (1950), pp. 87-110.
15. Parsons, C., “The impredicativity of induction,” pp. 132-54 in How Many Questions? Essays in Honor of Sidney Morgenbesser, edited by L. S. Cauman et al., Hackett, Indi-anapolis, 1983.
16. Parsons, T., “On the consistency of the first-order portion of Frege’s logical system,” Notre Dame Journal of Formal Logic, vol. 28 (1987), pp. 161-88.
17. Shoenfield, J., “A relative consistency proof,” The Journal of Symbolic Logic, vol. 19 (1954), pp. 21-28.
18. Skolem, T., “The foundations of elementary arithmetic,” pp. 302-33 in From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931, translated by S. BauerMengelberg, edited by J. van Heijenoort, Harvard University Press, Cambridge, 1967.
19. Skolem, T., Abstract Set Theory, Notre Dame Mathematical Lectures, Notre Dame, 1962.
20. Tarski, A., A. Mostowski, and R. M. Robinson, Undecidable Theories, North-Holland, Amsterdam, 1953.
21. Weyl, H., Das Kontinuum: Kritische Untersuchungen ber die Grundlagen der Analysis, Veit, Leipzig, 1918.
22. Whitehead, A. N., and B. Russell, Principia Mathematica, vol. 1, 2d edition, Cambridge University Press, Cambridge, 1925.