Selective ultrafilters on FIN

Zheng, Yuan Yuan

doi:10.1090/proc/13644

Selective ultrafilters on FIN
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by Yuan Yuan Zheng

Proc. Amer. Math. Soc. 145 (2017), 5071-5086

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 $\mathrm {FIN}$ 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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