• Corpus ID: 246996857

# On heights of distributivity matrices

@inproceedings{Fischer2022OnHO,
title={On heights of distributivity matrices},
author={Vera Fischer and Marlene Koelbing and Wolfgang Wohofsky},
year={2022}
}
• Published 18 February 2022
• Mathematics
We construct a model in which there exists a distributivity matrix of regular height λ larger than h; both λ = c and λ < c are possible. A distributivity matrix is a refining system of mad families without common refinement. Of particular interest in our proof is the preservation of B-Canjarness.
1 Citations
Games on base matrices
• Mathematics
• 2022
Using a game characterization of distributivity, we show that base matrices for P(ω)/fin of regular height larger than h necessarily have maximal branches which are not cofinal.

## References

SHOWING 1-10 OF 35 REFERENCES
A model in which the base-matrix tree cannot have cofinal branches
A model of ZFC is constructed in which the distributivity cardinal h is , and in which there are no ω 2 -towers in [ ω ] ω so that any base-matrix tree in this model has no cofinal branches.
Mad families, splitting families and large continuum
• Mathematics
The 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 .
A Sacks amoeba preserving distributivity of P(ω)/fin
• Mathematics
• 2019
By iterating the amoeba for Sacks forcing constructed implicitly in the paper “Borel partitions of infinite subtrees of a perfect tree” by Louveau, Shelah, and Veličković (Ann. Pure Appl. Logic,
On the Spectrum of Characters of Ultrafilters
• Mathematics
Notre Dame J. Formal Log.
• 2018
We show that the character spectrum $Sp_\chi(\lambda)$, for a singular cardinal $\lambda$ of countable cofinality, may include any prescribed set of regular cardinals between $\lambda$ and
Base Tree Property
• Mathematics
Order
• 2015
It is shown that every ρ-closed partial order of size continuum has a base tree and that σ-closed forcing notions of density 𝔠 correspond exactly to regular suborders of the collapsing algebra Coll(ω1, 2ω).
Some Forcing Techniques : Ultrapowers , templates , and submodels
This is an expository paper about several sophisticated forcing techniques closed related to standard finite support iterations of ccc partial orders. We focus on the four topics of ultrapowers of
THE CONSISTENCY OF ARBITRARILY LARGE SPREAD BETWEEN THE BOUNDING AND THE SPLITTING NUMBERS
In the following κ and λ are arbitrary regular uncountable cardinals. What was known? Theorem 1 (Balcar-Pelant-Simon, [2]). It is relatively consistent with ZFC that s = ω1 < b = κ. Theorem 2
centred forcing and reflection of (sub)metrizability
By using supercompact reflection and preservation lemmas for random real forcing and a-centred forcing, we obtain a model in which every normal Moore space is submetrizable, but not every normal