# Pseudo P-points and splitting number

@article{Dow2019PseudoPA, title={Pseudo P-points and splitting number}, author={Alan Dow and Saharon Shelah}, journal={Archive for Mathematical Logic}, year={2019}, pages={1-23} }

We construct a model in which the splitting number is large and every ultrafilter has a small subset with no pseudo-intersection.

## 4 Citations

### On the bounding, splitting, and distributivity numbers

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The cardinal invariants h, b, s of Ppωq are known to satisfy that ω1 ď h ď mintb, su. We prove that all inequalities can be strict. We also introduce a new upper bound for h and show that it can be…

### Maximal almost disjoint families and pseudocompactness of hyperspaces

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### LIST OF PUBLICATIONS

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1. Sh:a Saharon Shelah. Classification theory and the number of nonisomorphic models, volume 92 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam-New…

### Local thinning of 3D stereo images based on symmetric decryption algorithm

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## References

SHOWING 1-10 OF 18 REFERENCES

### Ultrafilters with small generating sets

- Mathematics
- 1989

It is consistent, relative to ZFC, that the minimum number of subsets ofω generating a non-principal ultrafilter is strictly smaller than the dominating number. In fact, these two numbers can be any…

### The almost-disjointness number may have countable cofinality

- Mathematics
- 2003

We show that it is consistent for the almost-disjointness number a to have countable cofinality. For example, it may be equal to N ω .

### Countable Fréchet Boolean groups: An independence result

- MathematicsThe Journal of Symbolic Logic
- 2009

Abstract It is relatively consistent with ZFC that every countable FUfin space of weight ℵ1 is metrizable. This provides a partial answer to a question of G. Gruenhage and P. Szeptycki [GS1].

### Mad families, splitting families and large continuum

- MathematicsThe Journal of Symbolic Logic
- 2011

Using a finite support iteration of ccc posets, if μ is a measurable cardinal and μ < κ < λ, then using similar techniques the authors obtain the consistency of .

### Adjoining dominating functions

- MathematicsJournal of Symbolic Logic
- 1985

Abstract If dominating functions in ω ω are adjoined repeatedly over a model of GCH via a finite-support c.c.c. iteration, then in the resulting generic extension there are no long towers, every…

### Ultrafilters on $\omega$-their ideals and their cardinal characteristics

- Mathematics
- 1997

For a free ultrafllterU on ! we study several cardinal characteristics which describe part of the combinatorial structure of U. We provide various consistency results; e.g. we show how to force…

### ULTRAFILTERS ON ! —THEIR IDEALS AND THEIR CARDINAL CHARACTERISTICS

- Mathematics
- 1997

. For a free ultra(cid:12)lter U on ω we study several cardinal characteristics which describe part of the combinatorial structure of U . We provide various consistency results; e.g. we show how to…

### On the generic existence of special ultrafilters

- Mathematics
- 1990

We introduce the concept of the generic existence of P-point, Qpoint, and selective ultrafilters, a concept which is somewhat stronger than the existence of these sorts of ultrafilters. We show that…