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Strong termination for the epsilon substitution method

Published online by Cambridge University Press:  12 March 2014

Grigori Mints
Grigori Mints*
Affiliation:
Department of Philosophy, Stanford University, Stanford, CA 94305, USA, E-mail: mints@csli.stanford.edu
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Abstract

Ackermann proved termination for a special order of reductions in Hilbert's epsilon substitution method for the first order arithmetic. We establish termination for arbitrary order of reductions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 4 , December 1996 , pp. 1193 - 1205
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1]Ackermann, W., Begründung des Tertium non datur mittels der Hilbertschen Theorie der Widerspruchsfreiheit, Mathematische Annalen, vol. 93 (1925), pp. 1–36.CrossRefGoogle Scholar
[2]Ackermann, W., Zur Widerspruchsfreiheit der Zahlentheorie, Mathematische Annalen, vol. 117 (1940), pp. 162–194.CrossRefGoogle Scholar
[3]Bourbaki, N., Theorie des ensembles, Hermann, 1958.Google Scholar
[4]Dragalin, A., Mathematical intuitionism, American Mathematical Society, 1988.Google Scholar
[5]Gentzen, G., Die Widerspruchsfreiheit der reinen Zahlentheorie, Mathematische Annalen, vol. 112 (1936), no. 4, pp. 493–565.CrossRefGoogle Scholar
[6]Girard, J.-Y., Une extension de l'interpretation de Gödela l'analyse et la application a l'elimination des coupures dans l'analyse et la theorie des types, Proceedings of the 2nd Scandinavian Logic Symposium, North-Holland, 1972, pp. 63–92.Google Scholar
[7]Hilbert, D., Probleme der Grundlegung der Mathematik, Mathematische Annalen, vol. 102 (1929), pp. 1–9.CrossRefGoogle Scholar
[8]Hilbert, D. and Bernays, P., Grundlagen der Mathematik, Bd. 2, Springer, 1970.CrossRefGoogle Scholar
[9]Kleene, S. C., Introduction to metamathematics, Van Nostrand, 1952.Google Scholar
[10]Kreisel, G., On the interpretation of non-finitist proofs I, this Journal, vol. 16 (1951), pp. 241–267.Google Scholar
[11]Kreisel, G., On the interpretation of non-finitist proofs II, this Journal, vol. 17 (1952), pp. 43–58.Google Scholar
[12]Mints, G., Simplified consistency proof for arithmetic, Proceedings of the Estonian Academy of Science Fiz.-Math., vol. 31 (1982), no. 4, pp. 376–382, in Russian.CrossRefGoogle Scholar
[13]Mints, G., Epsilon substitution method for the theory of hereditarily finite sets, Proceedings of the Estonian Academy of Science Fiz.-Math., vol. 38 (1989), no. 2, pp. 154–164, in Russian.CrossRefGoogle Scholar
[14]Mints, G., Hilbert's substitution method and Gentzen-type systems, Proceedings of 9th International Congress of Logic, Methodology and Philosophy of Science (Uppsala, Sweden) (Prawitz, D., Skyrms, B., and Westerstahl, D., editors), vol. IX, Elsevier Science B. V., 1994, pp. 91–122.Google Scholar
[15]Mints, G., Tupailo, S., and Buchholz, W., Epsilon substitution method for elementary analysis, Archive for Mathematical Logic, vol. 35 (1996), pp. 103–120.CrossRefGoogle Scholar
[16]Schutte, K., Proof theory, Springer, 1977.CrossRefGoogle Scholar
[17]Tait, W., Functionals defined by transfinite recursion, this Journal, vol. 30 (1965), no. 2, pp. 155–174.Google Scholar
[18]Tait, W., The substitution method, this Journal, vol. 30 (1965), no. 2, pp. 175–192.Google Scholar
[19]von Neumann, J., Zur Hilbertschen Beweistheorie, Mathematische Zeitschrift, vol. 26 (1927), pp. 1–46.CrossRefGoogle Scholar
[20]Weyl, H., David Hilbert and his mathematical work, Bulletin of the American Mathematical Society, vol. 50 (1944), pp. 612–654.CrossRefGoogle Scholar