First-order sentences in random groups II: $\forall\exists$-sentences
Logic
2022-12-23 v1 Group Theory
Abstract
We prove that a random group, in Gromov's density model with satisfies with overwhelming probability a universal-existential first-order sentence (in the language of groups) if and only if is true in a nonabelian free group.
Cite
@article{arxiv.2212.11780,
title = {First-order sentences in random groups II: $\forall\exists$-sentences},
author = {Olga Kharlampovich and Rizos Sklinos},
journal= {arXiv preprint arXiv:2212.11780},
year = {2022}
}