Long Strong Chains of Subsets of $\omega_1$

David Asperó; Curial Gallart

Long Strong Chains of Subsets of $\omega_1$

Logic 2026-04-20 v1

Authors: David Asperó , Curial Gallart

Abstract

We force the existence of a chain of length $\omega_3$ in $[\omega_1]^{\omega_1}$ increasing modulo finite. The construction involves symmetric systems of models of two types as side conditions, introduced by the second author. This improves previous results of Koszmider and Veli\v{c}kovi\'{c}-Venturi.

Keywords

chain of subsets $\omega_1$ finite modulo symmetric systems set theory

Cite

@article{arxiv.2604.15894,
  title  = {Long Strong Chains of Subsets of $\omega_1$},
  author = {David Asperó and Curial Gallart},
  journal= {arXiv preprint arXiv:2604.15894},
  year   = {2026}
}

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31 pages

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