Unthreadability with Small Conditions

Maxwell Levine

Unthreadability with Small Conditions

Logic 2026-03-17 v2

Authors: Maxwell Levine

Abstract

We introduce a forcing that adds a $\square(\aleph_2,\aleph_0)$ -sequence with countable conditions under CH. Assuming the consistency of a weakly compact cardinal, we can find a forcing extension by our new poset in which both $\square(\aleph_2,<\!\aleph_0)$ and $\square_{\aleph_1,\aleph_0}$ fail in the forcing extension.

Keywords

set theory forcing set theory

Cite

@article{arxiv.2209.12258,
  title  = {Unthreadability with Small Conditions},
  author = {Maxwell Levine},
  journal= {arXiv preprint arXiv:2209.12258},
  year   = {2026}
}

Comments

Tentative revision; more revisions are still needed, in particular for Section 3

Unthreadability with Small Conditions

Abstract

Keywords

Cite

Comments

Related papers