论文标题
有限生成的组的Galois动作很少有模型伴侣
Galois actions of finitely generated groups rarely have model companions
论文作者
论文摘要
We show that if $G$ is a finitely generated group such that its profinite completion $\widehat{G}$ is ``far from being projective'' (that is the kernel of the universal Frattini cover of $\widehat{G}$ is not a small profinite group), then the class of existentially closed $G$-actions on fields is not elementary.由于任何无限生成的，几乎是免费的，而且不是免费的群体'远非投影''，因此本文的主要结果纠正了我们论文中的错误``具有几乎免费的小组动作的领域模型理论''，proc''。伦敦数学。 Soc。，（2）118（2019），221--256在该论文中显示了定理3.26的否定。
We show that if $G$ is a finitely generated group such that its profinite completion $\widehat{G}$ is ``far from being projective'' (that is the kernel of the universal Frattini cover of $\widehat{G}$ is not a small profinite group), then the class of existentially closed $G$-actions on fields is not elementary. Since any infinite, finitely generated, virtually free, and not free group is ``far from being projective'', the main result of this paper corrects an error in our paper ``Model theory of fields with virtually free group actions'', Proc. London Math. Soc., (2) 118 (2019), 221--256 by showing the negation of Theorem 3.26 in that paper.
