Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-22T20:09:37.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Projective prewellorderings vs projective wellfounded relations

Published online by Cambridge University Press:  12 March 2014

Xianghui Shi
Xianghui Shi*
Affiliation:
Beijing Normal University, School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's, Republic Of China, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that it is relatively consistent with ZFC that there is aprojective wellfounded relation with rank higher than all projective prewellorderings.

Keywords

Prewellorderingwellfounded relationprojective ordinals
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 2 , June 2009 , pp. 579 - 596
Copyright
Copyright © Association for Symbolic Logic 2009

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]Erdős, Paul, Hajnal, Andras, and Rado, Richard, Partition relations for cardinal numbers. Acta Mathematica Academias Scientiarum Hungaricae, vol. 16 (1965), pp. 93–196.CrossRefGoogle Scholar
[2]Harrington, L. A., Long projective wellorderings, Annals of Mathematical Logic, vol. 12 (1977), pp. 1–24.CrossRefGoogle Scholar
[3]Jech, Thomas, Set Theory, 3rd (millenium, revised and expanded) ed., Springer, 2003.Google Scholar
[4]Kechris, Alexander S.. On projective ordinals, this Journal, vol. 39 (1974), no. 2, pp. 269–282.Google Scholar
[5]Kechris, Alexander S., Solovay, Robert M., and Steel, John R., The Axiom of Determinacy and the prewellordering property, Cabal Seminar '77–'79 (Proceedings of the Caltech-UCLA Logic Seminar, 1977-1979), Springer, 1981, pp. 101–125.Google Scholar
[6]Kunen, Kenneth, Set Theory: An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland, 1980.Google Scholar
[7]Moschovakis, Yiannis N., Determinacy and prewellorderings of the continuum, Mathematical Logic and Foundations of Set Theory (Bar-Hillel, Y., editor), North-Holland, 1970, pp. 24–62.Google Scholar
[8]Moschovakis, Yiannis N., Descriptive Set Theory, North-Holland Publishing Co., 1980.Google Scholar
[9]Shi, Xianghui, Prewellorderings vs wellfounded relations, Ph.D. thesis. University of California at Berkeley, 2006.Google Scholar