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A note on the normal filters extension property


Author: Yair Hayut
Journal: Proc. Amer. Math. Soc. 148 (2020), 3129-3133
MSC (2010): Primary 03E20; Secondary 03E55
DOI: https://doi.org/10.1090/proc/14939
Published electronically: March 18, 2020
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Abstract: We show that if $ \lambda ^{<\kappa } = \lambda $ and every normal filter on $ P_\kappa \lambda $ can be extended to a $ \kappa $-complete ultrafilter, then so does every $ \kappa $-complete filter on $ \lambda $. This answers a question of Gitik.


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Additional Information

Yair Hayut
Affiliation: Kurt Gödel Research Center, Institut für Mathematik, Universität Wien, Wien 1020, Austria
Email: yair.hayut@univie.ac.at

DOI: https://doi.org/10.1090/proc/14939
Received by editor(s): August 30, 2019
Received by editor(s) in revised form: October 29, 2019, and November 4, 2019
Published electronically: March 18, 2020
Additional Notes: This research was partially supported by the FWF Lise Meitner grant, 2650-N35
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2020 American Mathematical Society