English

On Namba Forcing and Minimal Collapses

Logic 2025-10-15 v1

Abstract

We build on a 1990 paper of Bukovsky and Coplakova-Hartova. First, we remove the hypothesis of CH\textsf{CH} from one of their minimality results. Then, using a measurable cardinal, we show that there is a 2V=1|\aleph_2^V|=\aleph_1-minimal extension that is not a 3V=1|\aleph_3^V|=\aleph_1-extension, answering the first of their questions.

Cite

@article{arxiv.2408.03487,
  title  = {On Namba Forcing and Minimal Collapses},
  author = {Maxwell Levine},
  journal= {arXiv preprint arXiv:2408.03487},
  year   = {2025}
}
R2 v1 2026-06-28T18:05:55.971Z