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Partitioning a reflecting stationary set


Authors: Maxwell Levine and Assaf Rinot
Journal: Proc. Amer. Math. Soc. 148 (2020), 3551-3565
MSC (2010): Primary 03E05; Secondary 03E04
DOI: https://doi.org/10.1090/proc/14783
Published electronically: May 4, 2020
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Abstract: We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinal combinatorics, we infer that it is never the case that there exists a singular cardinal all of whose scales are very good.


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Additional Information

Maxwell Levine
Affiliation: Universität Wien, Kurt Gödel Research Center for Mathematical Logic, Wien, Austria
Email: maxwell.levine@univie.ac.at

Assaf Rinot
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
Email: rinotas@math.biu.ac.il

DOI: https://doi.org/10.1090/proc/14783
Keywords: Reflecting stationary set, very good scale, Ulam matrix, club guessing
Received by editor(s): February 15, 2019
Received by editor(s) in revised form: July 19, 2019
Published electronically: May 4, 2020
Additional Notes: The second author was partially supported by the European Research Council (grant agreement ERC-2018-StG 802756) and by the Israel Science Foundation (grant agreement 2066/18).
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2020 American Mathematical Society