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The diagonal reflection principle


Author: Sean Cox
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
Published electronically: June 2, 2011
MathSciNet review: 2910775
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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$   cof$ (\omega)$ condenses correctly for many structures.


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Additional Information

Sean Cox
Affiliation: Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany
Email: sean.cox@uni-muenster.de

DOI: https://doi.org/10.1090/S0002-9939-2011-11103-1
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
Article copyright: © Copyright 2011 American Mathematical Society

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