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Ordinal diagrams for Π3-reflection

Published online by Cambridge University Press:  12 March 2014

Toshiyasu Arai
Toshiyasu Arai*
Affiliation:
Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan E-mail: arai@mis.hiroshima-u.ac.jp
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Abstract

In this paper we introduce a recursive notation system O(Π3) of ordinals. An element of the notation system is called an ordinal diagram. The system is designed for proof theoretic study of theories of Π3-reflection. We show that for each α < Ω in O(Π3) a set theory KP Π3 for Π3-reflection proves that the initial segment of O(Π3) determined by α is a well ordering. Proof theoretic study for such theories will be reported in [ 4].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 3 , September 2000 , pp. 1375 - 1394
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

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