First-order sentences in random groups II: -sentences

  • Olga Kharlampovich

    Hunter College and Graduate Center, CUNY, New York, USA
  • Rizos Sklinos

    Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing, P. R. China
First-order sentences in random groups II: $\forall\exists$-sentences cover
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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. It is remarked that one can also obtain the optimal result, that is, replace by .

Cite this article

Olga Kharlampovich, Rizos Sklinos, First-order sentences in random groups II: -sentences. Groups Geom. Dyn. (2025), published online first

DOI 10.4171/GGD/872