We show quantifier elimination theorems for real closed valued fields with separated analytic structure and overconvergent analytic structure in their natural one-sorted languages and deduce that such structures are weakly o-minimal. We also provide a short proof that algebraically closed valued fields with separated analytic structure (in any rank) are C-minimal.

中文翻译：

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具有解析结构的实闭值域

我们展示了具有分离解析结构和过收敛解析结构的实闭值域的量词消除定理，并推断出这些结构是弱 o-minimal 的。我们还提供了一个简短的证明，证明具有分离分析结构（任何等级）的代数闭值域是C-最小。