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 -stability for any cardinal . Not only the stability, it is known that his construction preserves various model-theoretic properties such as simplicity, NIP, and NTP. Inspired by the last result, we show that the construction also preserves NTP(NSOP) and NSOP. As a corollary, we obtain that if there is a theory of finite language which is non-simple NSOP, or which is NSOP but has SOP, 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