Geodesic
First-order sentences in random groups II: $\forall\exists$-sentences
Olga Kharlampovich1 orcid ; Rizos Sklinos2 orcid
1Hunter College and Graduate Center, CUNY, New York, USA
2Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing, P. R. China
Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 1107-1127

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DOI

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. It is remarked that one can also obtain the optimal result, that is, replace d<1/16 by d<1/2.
DOI : 10.4171/ggd/872
Classification : 03C60, 20F67
Mots-clés : random groups, first-order sentences

Olga Kharlampovich  1   ; Rizos Sklinos  2

1 Hunter College and Graduate Center, CUNY, New York, USA
2 Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing, P. R. China 
Olga Kharlampovich; Rizos Sklinos. First-order sentences in random groups II: $\forall\exists$-sentences. Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 1107-1127. doi: 10.4171/ggd/872
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     title = {First-order sentences in random groups {II:} $\forall\exists$-sentences},
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     year = {2025},
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