# On cardinal characteristics of Yorioka ideals

## TL;DR

This paper investigates the cardinal invariants of Yorioka ideals, constructing models where these invariants differ and comparing them to classical measure zero ideals, thus advancing understanding of their set-theoretic properties.

## Contribution

It constructs models demonstrating the pairwise distinctness of cardinal invariants for Yorioka ideals and compares these invariants to those of Lebesgue measure zero sets.

## Key findings

- Cardinal invariants of Yorioka ideals can be pairwise different.
- Additivity and cofinality of Yorioka ideals can differ from those of measure zero ideals.
- Models show these invariants do not necessarily coincide with classical measure zero ideals.

## Abstract

Yorioka [J. Symbolic Logic 67(4):1373-1384, 2002] introduced a class of ideals (parametrized by reals) on the Cantor space to prove that the relation between the size of the continuum and the cofinality of the strong measure zero ideal on the real line cannot be decided in ZFC. We construct a matrix iteration of ccc posets to force that, for many ideals in that class, their associated cardinal invariants (i.e. additivity, covering, uniformity and cofinality) are pairwise different. In addition, we show that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with the additivity and cofinality (respectively) of the ideal of Lebesgue measure zero subsets of the real line.