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Bounded stationary reflection


Authors: James Cummings and Chris Lambie-Hanson
Journal: Proc. Amer. Math. Soc. 144 (2016), 861-873
MSC (2010): Primary 03E05, 03E35, 03E55
DOI: https://doi.org/10.1090/proc12743
Published electronically: June 26, 2015
MathSciNet review: 3430860
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Abstract: We prove that, assuming large cardinals, it is consistent that there are many singular cardinals $ \mu $ such that every stationary subset of $ \mu ^+$ reflects but there are stationary subsets of $ \mu ^+$ that do not reflect at ordinals of arbitrarily high cofinality. This answers a question raised by Todd Eisworth.


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Additional Information

James Cummings
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email: jcumming@andrew.cmu.edu

Chris Lambie-Hanson
Affiliation: Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel
Email: clambiehanson@math.huji.ac.il

DOI: https://doi.org/10.1090/proc12743
Received by editor(s): January 31, 2014
Received by editor(s) in revised form: May 15, 2014, and January 22, 2015
Published electronically: June 26, 2015
Additional Notes: The first author was partially supported by NSF grant DMS-1101156.
The results in this paper form a part of the second author’s Ph.D. thesis.
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2015 American Mathematical Society