English

An example of a new simple theory

Logic 2019-07-29 v2

Abstract

We construct a countable simple theory which, in Keisler's order, is strictly above the random graph (but "barely so") and also in some sense orthogonal to the building blocks of the recently discovered infinite descending chain. As a result we prove in ZFC that there are incomparable classes in Keisler's order.

Keywords

Cite

@article{arxiv.1804.03254,
  title  = {An example of a new simple theory},
  author = {M. Malliaris and S. Shelah},
  journal= {arXiv preprint arXiv:1804.03254},
  year   = {2019}
}

Comments

30 pages. Section 4 and the appendices update some definitions and proofs from our earlier papers 1503.08341, 1404.2919 and 1208.2140 to the present context

R2 v1 2026-06-23T01:18:38.689Z