author={Vera Fischer and Sy-David Friedman and Diego Alejandro Mej{\'i}a and Diana Carolina Montoya},
  journal={The Journal of Symbolic Logic},
  pages={208 - 236}
Abstract We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations in Cichoń’s diagram, in particular, a model where the diagram can be separated into 7 different values. Furthermore, we show that this constellation of 7 values is consistent with the existence of a ${\rm{\Delta }}_3^1$ well-order of the reals. 

Matrix Iterations with Vertical Support Restrictions

  • D. Mej'ia
  • Mathematics
    Proceedings of the 14th and 15th Asian Logic Conferences
  • 2019
We use coherent systems of FS iterations on a power set, which can be seen as matrix iteration that allows restriction on arbitrary subsets of the vertical component, to prove general theorems about

Good projective witnesses

. We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it to show that consistently, the minimal cardinality a g of a maximal cofinitary group (MCG) is strictly


. We show that Miller partition forcing preserves selective independent families and P -points, which implies the consistency of cof ( N ) = a = u = i < a T = ω 2 . In addition, we show that Shelah’s

Some models produced by

We use the techniques in [BFII, \mathrm{M}\mathrm{e}\mathrm{j}\mathrm{l}3\mathrm{b} , FFMM] to construct models, by three‐ dimensional arrays of ccc posets, where many classical cardinal


A generic extension of Uri Abraham’s minimal $\Delta _3^1$ collapse function is defined by a real a, in which, for a given $n \ge 3$ is a lightface $\Pi _n^1 $ singleton, a effectively codes a cofinal map $\omega \to \omega _1^L $ minimal over L.

The ultrafilter and almost disjointness numbers

Cichoń’s diagram and localisation cardinals

This work reimplements the creature forcing construction used by Fischer et al. to separate Cichoń’s diagram into five cardinals as a countable support product, and adds uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.

On the bounding, splitting, and distributivity numbers

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

Cichoń’s maximum without large cardinals

Cichon's diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and $\sigma$-compact subsets

On cardinal characteristics of Yorioka ideals

It is shown that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with the addition and co finality of the ideal of Lebesgue measure zero subsets of the real line.



The left side of Cichoń’s diagram

Using a finite support iteration of ccc forcings, we construct a model of

Matrix iterations and Cichon’s diagram

Using matrix iterations of ccc posets, it is proved that it is consistent with ZFC to assign, at the same time, several arbitrary regular values on the left hand side of Cichon’s diagram.

Iterations of Boolean algebras with measure

It is shown that M is closed under iterations with finite support and that the forcing via such an algebra does not destroy the Lebesgue measure structure from the ground model, and a simple characterization of Martin's Axiom is deduced.

Mad families, splitting families and large continuum

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 .

Models of some cardinal invariants with large continuum (Forcing extensions and large cardinals)

We extend the applications of the techniques used in Arch Math Logic 52:261-278, 2013, to present various examples of consistency results where some cardinal invariants of the continuum take

Larger cardinals in Cichoń's diagram

  • J. Brendle
  • Mathematics
    Journal of Symbolic Logic
  • 1991
Abstract We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichoń's diagram are equal to κ while the others are equal to λ, where κ < λ are both