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Epsilon substitution method for -FIX

  • Toshiyasu Arai (a1)

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].

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[1]Ackermann, W., Zur Widerspruchsfreiheit der Zahlentheorie, Mathematische Annalen, vol. 117 (1940), pp. 162194.
[2]Arai, T., Ordinal diagrams for Π3-reflection, this Journal, vol. 65 (2000), pp. 13751394.
[3]Arai, T., Epsilon substitution method for theories of jump hierachies, Archive for Mathematical Logic, vol. 41 (2002), pp. 124154.
[4]Arai, T., Epsilon substitution method for , Annals of Pure and Applied Logic, vol. 121 (2003), pp. 163208.
[5]Arai, T., Proof theory for theories of ordinals II: Π3-Reflection, Annals of Pure and Applied Logic, vol. 129 (2004), pp. 3992.
[6]Arai, T., Wellfoundedness proofs by means of non-monotonic inductive definitions I: -operators, this Journal, vol. 69 (2004), pp. 830850.
[7]Arai, T., Epsilon substitution method for -FIX, Archive for Mathematical Logic, vol. 44 (2005), pp. 10091043.
[8]Arai, T., Ideas in the epsilon substitution method for -FIX, Annals of Pure and Applied Logic, vol. 136 (2005), pp. 321.
[9]Mints, G., Tupailo, S., and Buchholz, W., Epsilon substitution method for elementary analysis, Archive for Mathematical Logic, vol. 45 (1996), pp. 104140.
[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. 401481.
[11]Towsner, H., Epsilon substitution forID1, draft, 2004.
[12]Towsner, H., Epsilon substitution for transfinite induction, Archive for Mathematical Logic, vol. 44 (2005), pp. 397412.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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