Yorioka's characterization of the cofinality of the strong measure zero ideal and its independency from the continuum

TL;DR

This paper provides a simplified proof that the cofinality of the strong measure zero ideal cannot be definitively compared to the continuum within ZFC, highlighting its independence.

Contribution

It offers a more straightforward proof of the independence of the cofinality of the strong measure zero ideal from the continuum in ZFC.

Findings

No inequality between cof(SN) and c can be decided in ZFC.

Uses well-known techniques and results for the proof.

Simplifies previous proofs of this independence.

Abstract

In this paper we present a simpler proof of the fact that no inequality between $\mathrm{cof}(\mathcal{SN})$ and $\mathfrak{c}$ can be decided in ZFC by using well-known tecniques and results.