Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T18:47:28.694Z Has data issue: false hasContentIssue false
  • English
  • Français

CONSERVATIONS OF FIRST-ORDER REFLECTIONS

Published online by Cambridge University Press:  18 August 2014

TOSHIYASU ARAI
TOSHIYASU ARAI*
Affiliation:
GRADUATE SCHOOL OF SCIENCE CHIBA UNIVERSITY CHIBA, 263-8522, JAPANE-mail: tosarai@faculty.chiba-u.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

The set theory ΚΡΠN+1 for ΠN+1-reflecting universes is shown to be ΠN+1-conservative over iterations of ΠN-recursively Mahlo operations for each N ≥ 2.

Keywords

Reflecting ordinalsconservative extensions
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 3 , September 2014 , pp. 814 - 825
Copyright
Copyright © The Association for Symbolic Logic 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arai, T., Iterating the recursively mahlo operations, Proceedings of the thirteenth international congress of logic methodology, philosophy of science (Wei, W., Glymour, C., and Westerstahl, D., editors), College Publications, King’s College London, 2009, pp. 21–35.Google Scholar
Arai, T., Wellfoundedness proofs by means of non-monotonic inductive definitions II: First order operators. Annals of Pure and Applied Logic, vol. 162 (2010), pp. 107–143.Google Scholar
Arai, T., Proof theory of weak compactness. Journal of Mathematical Logic, vol. 13 (2013), p. 26.Google Scholar
Arai, T., Intuitionistic fixed point theories over set theories, submitted, arXiv: 1312.1133.Google Scholar
Arai, T., Lifting up the proof theory to the countables II: Second-order indescribable cardinals, in preparation.Google Scholar
Arai, T., Lifting up the proof theory to the countables: Zermelo-Fraenkel’s set theory, forthcoming.Google Scholar
Arai, T., Proof theory for theories of ordinals III: ΠN -reflection, to appear in the Gentzen’s centenary: the quest of consistency, Springer.Google Scholar
Barwise, J., Admissible sets and structures, Springer, Berlin, 1975.Google Scholar
Buchholz, W., A simplified version of local predicativity, Proof theory (Simmons, H., Aczel, P. H. G., and Wainer, S. S., editors), Cambridge UP, 1992, pp. 115–147.Google Scholar
Kreisel, G. and Lévy, A., Reflection principles and their use for establishing the complexity of axiomatic systems. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 14 (1968), pp. 97–142.Google Scholar
Rathjen, M., Proof theory of reflection. Annals of Pure and Applied Logic, vol. 68 (1994), pp. 181–224.Google Scholar
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, Amsterdam, 1974, pp. 301–381.Google Scholar
Schindler, R. and Zeman, M., Fine structure, Handbook of set theory (Foreman, M. and Kanamori, A., editors), vol. 1, Springer, 2010, pp. 605–656.Google Scholar