More separations of cardinal characteristics of the strong measure zero ideal

TL;DR

This paper introduces a new property of forcing notions to control the additivity of the null ideal, addressing open questions about cardinal characteristics related to strong measure zero sets.

Contribution

It presents a novel forcing property that allows precise manipulation of the additivity of the null ideal in finite support iterations.

Findings

Controlled the additivity of the null ideal using new forcing techniques

Answered open questions from prior research on cardinal characteristics

Developed methods for separating cardinal invariants of measure zero sets

Abstract

Let $\mathcal{N}$ be the $\sigma$-ideal of the null sets of reals. We introduce a new property of forcing notions that enable control of the additivity of $\mathcal{N}$ after finite support iterations. This is applied to answer some open questions from the work of Brendle, the first author, and Mej\'ia~\cite{BCM2}.