# The Next Best Thing to a P-Point

@article{Blass2015TheNB, title={The Next Best Thing to a P-Point}, author={Andreas Blass and Natasha Dobrinen and Dilip Raghavan}, journal={J. Symb. Log.}, year={2015}, volume={80}, pages={866-900} }

We study ultrafilters on $\omega^2$ produced by forcing with the quotient of $\scr P(\omega^2)$ by the Fubini square of the Fr\'echet filter on $\omega$. We show that such an ultrafilter is a weak P-point but not a P-point and that the only non-principal ultrafilters strictly below it in the Rudin-Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show… CONTINUE READING

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HIGHLY INFLUENTIAL

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