First-order sentences in random groups II: ∀∃-sentences

2022/12/22 by Kharlampovich, Olga, Sklinos, Rizos
#03C60 #20F67 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.2212.11780

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.

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