Corrigendum to "Measuring club-sequences together with the continuum large"

TL;DR

This paper corrects a previous flawed proof by providing a valid forcing construction that shows the consistency of a combinatorial principle called Measuring with a large continuum, over models of ZFC+CH.

Contribution

It offers a correct proof that Measuring can coexist with arbitrarily large continuum using a finite-support forcing with symmetric systems of models.

Findings

Established the consistency of Measuring with large continuum.

Developed a forcing construction over ZFC+CH.

Resolved a previously flawed proof in the literature.

Abstract

Measuring says that for e\-very sequence $(C_\delta)_{\delta<\omega_1}$ with each $C_\delta$ being a closed subset of $\delta$ there is a club $C\subseteq\omega_1$ such that for every $\delta\in C$, a tail of $C\cap\delta$ is either contained in or disjoint from $C_\delta$. In our JSL paper "Measuring club-sequences together with the continuum large" we claimed to prove the consistency of Measuring with $2^{\aleph_0}$ being arbitrarily large, thereby answering a question of Justin Moore. The proof in that paper was flawed. In the presented corrigendum we provide a correct proof of that result. The construction works over any model of ZFC+CH and can be described as the result of performing a finite-support forcing construction with side conditions consisting of suitable symmetric systems of models with markers.