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Dowker and super-Dowker filters


Authors: James Cummings and Charles Morgan
Journal: Proc. Amer. Math. Soc. 145 (2017), 5381-5390
MSC (2010): Primary 03E35; Secondary 03E55, 03E05
DOI: https://doi.org/10.1090/proc/13706
Published electronically: August 7, 2017
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Abstract: Our main results show that a very simple forcing construction can be used to add Dowker and super-Dowker filters:

  • Let $ \kappa $ be uncountable with $ \kappa ^{ < \kappa }=\kappa $. Let $ G$ be generic over $ V$ for $ Add(\kappa , \kappa ^{++})$. Then in $ V[G]$ there is a Dowker filter on $ \kappa ^+$.

  • Let $ V$ be Laver's model in which $ \kappa $ is supercompact and the supercompactness of $ \kappa $ is indestructible under $ \kappa $-directed closed forcing, and let $ G$ be generic for $ Add(\kappa , \kappa ^{++})$. Then in $ V[G]$ there is a super-Dowker filter on $ \kappa ^+$.


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Additional Information

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

Charles Morgan
Affiliation: Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom
Email: charles.morgan@ucl.ac.uk

DOI: https://doi.org/10.1090/proc/13706
Keywords: Dowker filter, super-Dowker filter, supercompact cardinal, forcing
Received by editor(s): June 20, 2016
Received by editor(s) in revised form: January 12, 2017
Published electronically: August 7, 2017
Additional Notes: The first author was partially supported by NSF grant DMS-1500790.
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2017 American Mathematical Society

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