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Selective ultrafilters on FIN


Author: Yuan Yuan Zheng
Journal: Proc. Amer. Math. Soc. 145 (2017), 5071-5086
MSC (2010): Primary 05D10; Secondary 03E02, 03E40
DOI: https://doi.org/10.1090/proc/13644
Published electronically: June 16, 2017
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Abstract: We consider selective ultrafilters on the collection $ \textnormal {FIN}$ of all finite nonempty subsets of $ \mathbb{N}$. If countable-support side-by-side Sacks forcing is applied, then every selective ultrafilter in the ground model generates a selective ultrafilter in the extension. We also show that selective ultrafilters localize the Parametrized Milliken Theorem, and that selective ultrafilters are Ramsey.


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Additional Information

Yuan Yuan Zheng
Affiliation: Department of Mathematics, University of Toronto, Room 6290, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
Email: yyz22@math.utoronto.ca

DOI: https://doi.org/10.1090/proc/13644
Received by editor(s): December 7, 2015
Received by editor(s) in revised form: November 12, 2016, and December 28, 2016
Published electronically: June 16, 2017
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2017 American Mathematical Society

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