Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T20:36:48.716Z Has data issue: false hasContentIssue false
  • English
  • Français

Transfinite dependent choice and ω-model reflection

Published online by Cambridge University Press:  12 March 2014

Christian Rüede
Christian Rüede*
Affiliation:
Sustenweg 2, 8048 Zürich, Switzerland, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we present some metapredicative subsystems of analysis. We deal with reflection principles, ω-model existence axioms (limit axioms) and axioms asserting the existence of hierarchies. We show several equivalences among the introduced subsystems. In particular we prove the equivalence of Σ11 transfinite dependent choice and Π21 reflection on ω-models of Σ11-DC.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 3 , September 2002 , pp. 1153 - 1168
Copyright
Copyright © Association for Symbolic Logic 2002

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

[1]Avigad, J., On the relationship between ATR0 and , this Journal, vol. 61 (1996), no. 3, pp. 768–779.Google Scholar
[2]Hirst, J. L., Reverse mathematics and ordinal exponentiation, Annals of Pure and Applied Logic, vol. 66 (1994), pp. 1–18.CrossRefGoogle Scholar
[3]Jäger, G., Theories for iterated jumps, handwritten notes, 1980.Google Scholar
[4]Jäger, G., Kahle, R., Setzer, A., and Strahm, T., The proof-theoretic analysis of transfinitely iterated fixed points theories, this Journal, vol. 64 (1999), pp. 53–67.Google Scholar
[5]Jäger, G. and Strahm, T., Fixed point theories and dependent choice, Archive for Mathematical Logic, vol. 39 (2000), pp. 493–508.Google Scholar
[6]Jäger, G. and Strahm, T., Upper bounds for metapredicative Mahlo in explicit mathematics and admissible set theory, this Journal, to appear.Google Scholar
[7]Kahle, R., Applikative Theorien und Frege-Strukturen, Ph.D. thesis, Institut für Informatik und angewandte Mathematik, Universität Bern, 1997.Google Scholar
[8]Rathjen, M., The strength of Martin-Löf type theory with a superuniverse. Part I, Archive for Mathematical Logic, vol. 39 (2000), no. 1, pp. 1–39.CrossRefGoogle Scholar
[9]Rüede, C., Metapredicative subsystem of analysis, Ph.D. thesis, Institut für Informatik und angewandte Mathematik, Universität Bern, 2000.Google Scholar
[10]Simpson, S. G., Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer Verlag, 1998.Google Scholar
[11]Strahm, T., First steps intometapredicativity in explicit mathematics, Sets and proofs (Cooper, S. B. and Truss, J., editors), Eds. Cambridge University Press, 1999, pp. 383–402.CrossRefGoogle Scholar
[12]Strahm, T., Autonomous fixed point progressions and fixed point transfinite recursion, Logic colloquium '98 (Buss, S., Hajek, P., and Pudlák, P., editors), vol. 13, ASL Lecture notes in Logic, 2000.Google Scholar
[13]Strahm, T., Wellordering proofs for metapredicative Mahlo, submitted.Google Scholar