The diagonal reflection principle
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Abstract:
We introduce a highly simultaneous version of stationary set reflection, called the Diagonal Reflection Principle (DRP). We prove that $PFA^{+\omega _1}$ implies DRP, and DRP in turn implies that the nonstationary ideal on $[\theta ]^\omega$ condenses correctly for many structures. We also prove that MM implies a weaker version of DRP, which in turn implies that the nonstationary ideal on $\theta \cap \text {cof}(\omega )$ condenses correctly for many structures.References
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Additional Information
- Sean Cox
- Affiliation: Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany
- MR Author ID: 883409
- Email: sean.cox@uni-muenster.de
- Received by editor(s): November 11, 2010
- Received by editor(s) in revised form: March 2, 2011
- Published electronically: June 2, 2011
- Additional Notes: I thank Matt Foreman, Ralf Schindler, and Martin Zeman for helpful conversations on related topics.
- Communicated by: Julia Knight
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 2893-2902
- MSC (2010): Primary 03E05, 03E50, 03E57
- DOI: https://doi.org/10.1090/S0002-9939-2011-11103-1
- MathSciNet review: 2910775