Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 05D10, 03E02, 03E40

Retrieve articles in all journals with MSC (2010): 05D10, 03E02, 03E40


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

American Mathematical Society