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Separating stationary reflection principles

Published online by Cambridge University Press:  12 March 2014

Paul Larson*
Affiliation:
Equipe de Logique, Université ParisVII, 2 Place Jussieu, Paris 75251, Cedex, France, E-mail: larson@logique.jussieu.fr

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
Copyright
Copyright © Association for Symbolic Logic 2000

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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. 137158.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. 237257.CrossRefGoogle Scholar
[5]Feng, Q., Projective stationary sets, and strong reflection principles, Journal of London Mathematical Society, vol. (2) 58 (1998), pp. 271283.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. 147.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. 360367.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. 256284.CrossRefGoogle Scholar
[13]Woodin, W.H., The axiom of determinacy, forcing axioms, and the nonstationary ideal, in preparation.Google Scholar