大场的随机生成子场
Existentially generated subfields of large fields
摘要：
我们研究由无限个存在可定义子集生成的大域的子域。我们说这样的子域是存在生成的。设$L$是一个特征指数为$p$的大域，$E\subseteq L$是一个存在生成的无限子域.我们发现，$E$包含$L^{(p^{n})}$，在$L$的$p^{n}$次幂，对于某些$n<ω$。这推广了Fehm的一个结果，该结果在假设$L$是完美的情况下显示了$E=L$。我们的方法是首先研究hensel域的存在生成子域。由于$L$在Hensel域$L((t))$中是存在闭的，我们的结果如下。
英文摘要：
We study subfields of large fields which are generated by infinite existentially definable subsets. We say that such subfields are existentially generated. Let $L$ be a large field of characteristic exponent $p$, and let $E\subseteq L$ be an infinite existentially generated subfield. We show that $E$ contains $L^{(p^{n})}$, the $p^{n}$-th powers in $L$, for some $n<ω$. This generalises a result of Fehm, which shows $E=L$ under the assumption that $L$ is perfect. Our method is to first study existentially generated subfields of henselian fields. Since $L$ is existentially closed in the henselian field $L((t))$, our result follows.
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