# 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}
}
• Published in J. Symb. Log. 2015
• Mathematics, Computer Science
• 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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#### Citations

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 16 REFERENCES

## Cofinal types of ultrafilters

• Computer Science, Mathematics
• Ann. Pure Appl. Log.
• 2012
VIEW 9 EXCERPTS

## A Model-Theoretic View of Some Special Ultrafilters

VIEW 6 EXCERPTS

## Tukey types of ultrafilters

• Mathematics
• 2011
VIEW 10 EXCERPTS

## Souslin partitions of products of finite sets

• Mathematics
• 2003
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

## Local Ramsey theory: an abstract approach

• Mathematics, Computer Science
• Math. Log. Q.
• 2017
VIEW 1 EXCERPT

## A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters, Part 2

• Mathematics
• 2012
VIEW 2 EXCERPTS

## The generic ultrafilter added by ${(\FIN \times \FIN)}^{+}$

VIEW 2 EXCERPTS

## Continuous cofinal maps on ultrafilters

VIEW 1 EXCERPT

## Distributivity of Quotients of Countable Products of Boolean Algebras

VIEW 2 EXCERPTS

## COFINAL TYPES OF TOPOLOGICAL DIRECTED ORDERS

• Mathematics
• 2004
VIEW 1 EXCERPT