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Wellfoundedness proofs by means of non-monotonic inductive definitions I: Π20-operators

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: [email protected]
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Abstract.

In this paper, we prove the wellfoundedrtess of recursive notation systems for reflecting ordinals up to Π3-reflection by relevant inductive definitions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 3 , September 2004 , pp. 830 - 850
Copyright
Copyright © Association for Symbolic Logic 2004

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References

REFERENCES

[1]Arai, T., Ordinal diagrams for Π3-reflection, this Journal, vol. 65 (2000), pp. 1375–1394.Google Scholar
[2]Arai, T., Ordinal diagrams for recursively Mahlo universes, Archive for Mathematical Logic, vol. 39 (2000), pp. 353–391.CrossRefGoogle Scholar
[3]Arai, T., Proof theory for theories of ordinals I: Recursively Mahlo ordinals, Annals of Pure and Applied Logic, vol. 122 (2003), pp. 1–85.CrossRefGoogle Scholar
[4]Arai, T., Proof theory for theories of ordinals II: Π3-reflection, Annals of Pure and Applied Logic, to appear.Google Scholar
[5]Arai, T., Proof theory for reflecting ordinals III: ΠN-reflection, submitted.Google Scholar
[6]Arai, T., Wellfoundedness proofs by means of non-monotonic inductive definitions II: First order operators,submitted.Google Scholar
[7]Arai, T., Ordinal diagrams for ΠN-reflection, draft.Google Scholar
[8]Buchholz, W., Normalfunktionen und konstruktive Systeme von Ordinalzahlen, Proof Theory Symposion, Kiel 1974 (Diller, J. and Müller, G. H., editors), Lecture Notes in Mathematics, vol. 500, Springer, 1975, pp. 4–25.Google Scholar
[9]Buchholz, W., Review of the paper: A. Setzer, Well-ordering proofs for Martin-Löf type theory, The Bulletin of Symbolic Logic, vol. 6 (2000), pp. 478–479.CrossRefGoogle Scholar
[10]Richter, W. H. and Aczel, P., Inductive definitions and reflecting properties of admissible ordinals, Generalized Recursion Theory, Studies in Logic, vol. 79, North-Holland, 1974, pp. 301–381.Google Scholar