## 16 Citations

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

- Mathematics
- 2022

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…

### On well-splitting posets

- MathematicsArchive for Mathematical Logic
- 2022

. We introduce a class of proper posets which is preserved under countable support iterations, includes ω ω -bounding, Cohen, Miller, and Mathias posets associated to ﬁlters with the Hurewicz…

### The almost disjointness invariant for products of ideals

- Mathematics
- 2021

. The almost disjointness numbers associated to the quotients determined by the transﬁnite products of the ideal of ﬁnite sets are investigated. A ZFC lower bound involving the minimum of the…

### ON THE BOUNDING, SPLITTING, AND DISTRIBUTIVITY NUMBERS OF P(N); AN APPLICATION OF LONG-LOW ITERATIONS

- Mathematics
- 2016

The cardinal invariants t, h, b, s of P(N) are known to satisfy that ω1 ≤ t ≤ h ≤ min{b, s} and that b < s and s < b are both consistent. We prove the consistency of each of the following…

### Partition calculus and cardinal invariants

- Mathematics
- 2014

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive…

### Combinatorial properties of MAD families

- Mathematics
- 2016

. We study some strong combinatorial properties of MAD families. An ideal I is Shelah-Stepr¯ans if for every set X ⊆ [ ω ] <ω there is an element of I that either intersects every set in X or…

### Template iterations with non-definable ccc forcing notions

- MathematicsAnn. Pure Appl. Log.
- 2015

### Splitting, Bounding, and Almost Disjointness Can Be Quite Different

- MathematicsCanadian Journal of Mathematics
- 2017

Abstract We prove the consistency of $$~~\text{add}\left( \mathcal{N} \right)<\operatorname{cov}\left( \mathcal{N} \right)<\mathfrak{p}\text{=}\mathfrak{s}\text{=}\mathfrak{g}< \text{add}\left(…

## References

SHOWING 1-10 OF 16 REFERENCES

### Comparing the closed almost disjointness and dominating numbers

- Mathematics
- 2011

We prove that if there is a dominating family of size א1, then there are א1 many compact subsets of ω whose union is a maximal almost disjoint family of functions that is also maximal with respect to…

### Mad Families Constructed from Perfect Almost Disjoint Families

- MathematicsThe Journal of Symbolic Logic
- 2013

The consistency of is proved together with the existence of a -definable mad family, answering a question posed by Friedman and Zdomskyy in [7, Question 16], and a new cardinal invariant is isolated, the Borel almost-disjointness number.

### Partition calculus and cardinal invariants

- Mathematics
- 2014

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive…

### 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…

### Mob families and mad families

- MathematicsArch. Math. Log.
- 1998

The consistency of ${\frak o} <{\frak d}$ is shown, where Â£o$ is the size of the smallest off-branch family, and ${ frak d$ is as usual the dominating number.

### Combinatorial Aspects of the Splitting Number

- Mathematics
- 2012

This paper deals with the splitting number $${\mathfrak{s}}$$ and polarized partition relations. In the first section we define the notion of strong splitting families, and prove that its existence…

### Proper and Improper Forcing

- Economics
- 1998

This work deals with set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. Consequently, the theory of iterated…

### Handbook of Set Theory

- Mathematics
- 2010

Handbook of Set Theory, Volume I, Akihiro Kanamori, 0. Introduction Thomas Jech, 1. Stationary Sets Andras Hajnal and Jean Larson, 2. Partition Relations Stevo Todorcevic, 3. Coherent Sequences Greg…

### Strong Polarized Relations for the Continuum

- Physics, Mathematics
- 2012

We prove that the strong polarized relation $${\left(\begin{array}{ll} 2^\mu\\ \mu \end{array}\right)\rightarrow \left(\begin{array}{ll} 2^\mu\\ \mu \end{array}\right)^{1,1}_2}$$ is consistent with…