First-order sentences in random groups I: universal sentences
Group Theory
2024-10-29 v3 Logic
Abstract
We prove that a random group, in Gromov's density model with , satisfies a universal sentence (in the language of groups) if and only if is true in a nonabelian free group.
Cite
@article{arxiv.2106.05461,
title = {First-order sentences in random groups I: universal sentences},
author = {O. Kharlampovich and R. Sklinos},
journal= {arXiv preprint arXiv:2106.05461},
year = {2024}
}
Comments
Second version, minor changes and in addition the main result has been extended to include constants