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About the proof-theoretic ordinals of weak fixed point theories

Published online by Cambridge University Press:  12 March 2014

Gerhard Jäger
Institut für Informatik und Angewandte Mathematik, Universität Bern, 3012 Bern, Switzerland, E-mail:
Barbara Primo
Mathematics Department, Eidgenössische Technische Hochschule, 8092 Zurich, Switzerland


This paper presents several proof-theoretic results concerning weak fixed point theories over second order number theory with arithmetic comprehension and full or restricted induction on the natural numbers. It is also shown that there are natural second order theories which are proof-theoretically equivalent but have different proof-theoretic ordinals.

Research Article
Copyright © Association for Symbolic Logic 1992

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[1]Beeson, M. J., Foundations of constructive mathematics, Springer-Verlag, Berlin, 1985.CrossRefGoogle Scholar
[2]Buchholz, W., Feferman, S., Pohlers, W., and Sieg, W., Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies, Lecture Notes in Mathematics, vol. 897, Springer-Verlag, Berlin, 1981.Google Scholar
[3]Feferman, S., Iterated inductive fixed-point theories: application to Hancock's conjecture, Patras logic symposion (Metakides, G., editor), North-Holland, Amsterdam, 1982, pp. 171196.CrossRefGoogle Scholar
[4]Feferman, S., Monotone inductive definitions, The L. E. J. Brouwer centenary symposium (Troelstra, A. S. and van Dalen, D., editors), North-Holland, Amsterdam, 1982, pp. 7789.Google Scholar
[5]Friedman, H., Iterated inductive definitions and -AC, Intuitionism and Proof Theory (Kino, al., editors), North-Holland, Amsterdam, 1970, pp. 435442.Google Scholar
[6]Girard, J.-Y., Proof theory and logical complexity. Vol. I, Bibliopolis, Napoli, 1987.Google Scholar
[7]Jäger, G., Iterating admissibility in proof theory, Proceedings of the Herbrand symposium/Logic Colloquium '81 (Stern, J., editor), North-Holland, Amsterdam, 1982, pp. 137146.CrossRefGoogle Scholar
[8]Jäger, G. and Stärk, R. F., The defining power of stratified and hierarchical logic programs, Proceedings of the triennial meeting of S. I. L. F. S. (Viareggio, 1990) (to appear).Google Scholar
[9]Lloyd, J. W., Foundations of logic programming, 2nd ed., Springer-Verlag, Berlin, 1987.CrossRefGoogle Scholar
[10]Moschovakis, Y. N., Elementary induction on abstract structures, North-Holland, Amsterdam, 1974.Google Scholar
[11]Primo, B., Überlegungen zur logischen Analyse von Fixpunkt-Theorien, Diplomarbeit, ETH, Zürich, 1988.Google Scholar
[12]Schütte, K., Proof theory, Springer-Verlag, Berlin, 1977.CrossRefGoogle Scholar
[13]Tait, W. W., Normal derivability in classical logic, The syntax and semantics of infinitary languages (Barwise, J., editor), Lecture Notes in Mathematics, vol. 72, Springer-Verlag, Berlin, 1968, pp. 204236.CrossRefGoogle Scholar
[14]Takeuti, G., Proof theory, 2nd ed., North-Holland, Amsterdam, 1987.Google Scholar