Non-$\forall$-homogeneity in free groups
Logic
2020-01-28 v1 Group Theory
Abstract
We prove that non-abelian free groups of finite rank at least 3 or of countable rank are not -homogeneous. We answer three open questions from Kharlampovich, Myasnikov, and Sklinos regarding whether free groups, finitely generated elementary free groups, and non-abelian limit groups form special kinds of Fra\"iss\'e classes in which embeddings must preserve -formulas. We also provide interesting examples of countable non-finitely generated elementary free groups.
Cite
@article{arxiv.2001.09904,
title = {Non-$\forall$-homogeneity in free groups},
author = {Olga Kharlampovich and Christopher Natoli},
journal= {arXiv preprint arXiv:2001.09904},
year = {2020}
}