English

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 d<1/16d<1/16, satisfies a universal sentence σ\sigma (in the language of groups) if and only if σ\sigma is true in a nonabelian free group.

Keywords

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

R2 v1 2026-06-24T03:02:17.758Z