English

When does $\aleph_1$-categoricity imply $\omega$-stability?

Logic 2024-08-14 v1

Abstract

For an 1\aleph_1-categorical atomic class, we clarify the space of types over the unique model of size 1\aleph_1. Using these results, we prove that if such a class has a model of size 1+\beth_1^+ then it is ω\omega-stable.

Keywords

Cite

@article{arxiv.2308.13942,
  title  = {When does $\aleph_1$-categoricity imply $\omega$-stability?},
  author = {John T. Baldwin and M. C. Laskowski and Saharon Shelah},
  journal= {arXiv preprint arXiv:2308.13942},
  year   = {2024}
}

Comments

22 pages

R2 v1 2026-06-28T12:05:09.360Z