p极闭域中fsg$\text｛fsg｝$群的一个注记

Pub Date : 2023-05-24 DOI:10.1002/malq.202200026

Will Johnson

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引用次数: 0

摘要

设G是p-自由闭域M中的可定义群。我们证明了G具有有限可满足泛型（fsg$\text{fsg}$）当且仅当G是可定义紧致的。案例M=Q p$M=\mathbb{Q}_pOnshuus和Pillay之前已经证明了$。

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A note on fsg $\text{fsg}$ groups in p-adically closed fields

Let G be a definable group in a p-adically closed field M. We show that G has finitely satisfiable generics ( $fsg$ ) if and only if G is definably compact. The case $M = Q_{p}$ was previously proved by Onshuus and Pillay.

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