English

Mekler's construction and tree properties

Logic 2020-05-04 v2

Abstract

Mekler constructed a way to produce a pure group from any given structure where the construction preserves κ\kappa-stability for any cardinal κ\kappa. Not only the stability, it is known that his construction preserves various model-theoretic properties such as simplicity, NIP, and NTP2_2. Inspired by the last result, we show that the construction also preserves NTP1_1(NSOP2_2) and NSOP1_1. As a corollary, we obtain that if there is a theory of finite language which is non-simple NSOP1_1, or which is NSOP2_2 but has SOP1_1, then there is a pure group theory with the same properties, respectively.

Cite

@article{arxiv.1903.07087,
  title  = {Mekler's construction and tree properties},
  author = {JinHoo Ahn},
  journal= {arXiv preprint arXiv:1903.07087},
  year   = {2020}
}

Comments

11 pages

R2 v1 2026-06-23T08:10:34.824Z