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Epsilon substitution method for -FIX

Published online by Cambridge University Press:  12 March 2014

Toshiyasu Arai
Toshiyasu Arai*
Affiliation:
Graduate School of Science and Technology, Kobe University, Rokko-Dai, Nada-Ku, Kobe 657-8501, Japan, E-mail: arai@kurt.scitec.kobe-u.ac.jp
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Abstract

In this paper we formulate epsilon substitution method for a theory -FIX for nonmonotonic inductive definitions. Then we give a termination proof of the H-processes based on Ackermann [1].

Keywords

epsilon substitution; ordinal interpretation; termination proof
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 4 , December 2006 , pp. 1155 - 1188
Copyright
Copyright © Association for Symbolic Logic 2006

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References

REFERENCES

[1]Ackermann, W., Zur Widerspruchsfreiheit der Zahlentheorie, Mathematische Annalen, vol. 117 (1940), pp. 162–194.CrossRefGoogle Scholar
[2]Arai, T., Ordinal diagrams for Π3-reflection, this Journal, vol. 65 (2000), pp. 1375–1394.Google Scholar
[3]Arai, T., Epsilon substitution method for theories of jump hierachies, Archive for Mathematical Logic, vol. 41 (2002), pp. 124–154.CrossRefGoogle Scholar
[4]Arai, T., Epsilon substitution method for , Annals of Pure and Applied Logic, vol. 121 (2003), pp. 163–208.CrossRefGoogle Scholar
[5]Arai, T., Proof theory for theories of ordinals II: Π3-Reflection, Annals of Pure and Applied Logic, vol. 129 (2004), pp. 39–92.CrossRefGoogle Scholar
[6]Arai, T., Wellfoundedness proofs by means of non-monotonic inductive definitions I: -operators, this Journal, vol. 69 (2004), pp. 830–850.Google Scholar
[7]Arai, T., Epsilon substitution method for -FIX, Archive for Mathematical Logic, vol. 44 (2005), pp. 1009–1043.CrossRefGoogle Scholar
[8]Arai, T., Ideas in the epsilon substitution method for -FIX, Annals of Pure and Applied Logic, vol. 136 (2005), pp. 3–21.CrossRefGoogle Scholar
[9]Mints, G., Tupailo, S., and Buchholz, W., Epsilon substitution method for elementary analysis, Archive for Mathematical Logic, vol. 45 (1996), pp. 104–140.Google Scholar
[10]Richter, W. H. and Aczel, P., Inductive definitions and reflecting properties of admissible ordinals, Generalized recursion theory (Fenstad, J. E. and Hinman, P. G., editors), Studies in Logic, vol. 79, North Holland, 1974, pp. 401–481.Google Scholar
[11]Towsner, H., Epsilon substitution forID1, draft, 2004.Google Scholar
[12]Towsner, H., Epsilon substitution for transfinite induction, Archive for Mathematical Logic, vol. 44 (2005), pp. 397–412.CrossRefGoogle Scholar