English

Strongly increasing sequences

Logic 2026-04-01 v4

Abstract

Using a variation of Woodin's Pmax\mathbb{P}_{\mathrm{max}} forcing, we force over a model of the Axiom of Determinacy to produce a model of ZFC containing a very strongly increasing sequence of length ω2\omega_{2} consisting of functions from ω\omega to ω\omega. We also show that there can be no such sequence of length ω4\omega_{4}.

Keywords

Cite

@article{arxiv.2503.06758,
  title  = {Strongly increasing sequences},
  author = {Paul B. Larson and Chris Lambie-Hanson},
  journal= {arXiv preprint arXiv:2503.06758},
  year   = {2026}
}
R2 v1 2026-06-28T22:13:08.418Z