English

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

Logic 2021-08-19 v2

Abstract

Measuring says that for e\-very sequence (Cδ)δ<ω1(C_\delta)_{\delta<\omega_1} with each CδC_\delta being a closed subset of δ\delta there is a club Cω1C\subseteq\omega_1 such that for every δC\delta\in C, a tail of CδC\cap\delta is either contained in or disjoint from CδC_\delta. In our JSL paper "Measuring club-sequences together with the continuum large" we claimed to prove the consistency of Measuring with 202^{\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.

Keywords

Cite

@article{arxiv.2012.07843,
  title  = {Corrigendum to "Measuring club-sequences together with the continuum large"},
  author = {David Aspero and Miguel Angel Mota},
  journal= {arXiv preprint arXiv:2012.07843},
  year   = {2021}
}

Comments

21 pages. arXiv admin note: substantial text overlap with arXiv:1712.07724

R2 v1 2026-06-23T20:57:58.072Z