Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T18:12:02.045Z Has data issue: false hasContentIssue false
  • English
  • Français

Separating stationary reflection principles

Published online by Cambridge University Press:  12 March 2014

Paul Larson
Paul Larson*
Affiliation:
Equipe de Logique, Université ParisVII, 2 Place Jussieu, Paris 75251, Cedex, France, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a variety of (ω, ∞)-distributive forcings which when applied to models of Martin's Maximum separate certain well known reflection principles. In particular, we do this for the reflection principles SR, SRα (α ≤ ω1), and SRP.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 1 , March 2000 , pp. 247 - 258
Copyright
Copyright © Association for Symbolic Logic 2000

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]Baumgartner, J.E., Hajnal, A., and Máté, A., Weak saturation properties of ideals, Infinite and finite sets, vol. I (Hajnal, A., Rado, R., and Sós, V.T., editors), North-Holland, Amsterdam/London, 1975, pp. 137–158.Google Scholar
[2]Bekkali, M., Topics in set theory, Lecture Notes in Mathematics, vol. 1476, Springer-Verlag, New York/Berlin, 1991.CrossRefGoogle Scholar
[3]Feng, Q., Strongly Baire trees and a cofinal branch principle, in preparation.Google Scholar
[4]Feng, Q. and Jech, T., Local clubs, reflection, and preserving stationary sets, Proceedings of London Mathematical Society, vol. (3) 58 (1989), pp. 237–257.CrossRefGoogle Scholar
[5]Feng, Q., Projective stationary sets, and strong reflection principles, Journal of London Mathematical Society, vol. (2) 58 (1998), pp. 271–283.CrossRefGoogle Scholar
[6]Foreman, M., Magidor, M., and Shelah, S., Martin's Maximum, saturated ideals, and non-regular ultrafilters. Part I, Annals of Mathematics, vol. 127 (1988), pp. 1–47.CrossRefGoogle Scholar
[7]Jech, T., Set theory, Academic Press, 1978.Google Scholar
[8]Larson, P., The size , Archive for Mathematical Logic (to appear).Google Scholar
[9]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, New York/Berlin, 1982.CrossRefGoogle Scholar
[10]Shelah, S., SPFA implies MM, but not PFA+, this Journal, vol. 52, No. 2 (1987), pp. 360–367.Google Scholar
[11]Todorčević, S., Strong reflection principles, circulated notes.Google Scholar
[12]Veličković, Boban, Forcing axioms and stationary sets, Advances in Mathematics, vol. 94 (1992), pp. 256–284.CrossRefGoogle Scholar
[13]Woodin, W.H., The axiom of determinacy, forcing axioms, and the nonstationary ideal, in preparation.Google Scholar