Submission date: 22 December 2022.

Abstract:

We prove that a random group, in Gromov's density model with d < 1/16 satisfies with overwhelming probability a universal-existential first-order sentence σ (in the language of groups) if and only if σ is true in a nonabelian free group.

Mathematics Subject Classification: 03C60, 20F67

Keywords and phrases:

Full text arXiv 2212.11780: pdf, ps.