In this note, we construct a distal expansion for the structure $$\left( {; + , < ,H} \right)$$, where $H \subseteq $ is a dense $Q$-vector space basis of $R$ (a so-called Hamel basis). Our construction is also an expansion of the dense pair $\left( {; + , < ,} \right)$ and has full quantifier elimination in a natural language.

中文翻译：

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HAMEL 空间和远端扩展

在本说明中，我们构建了结构的远端扩展$$\left( {; + , < ,H} \right)$$， 在哪里$H \子集$是稠密的$Q$-向量空间基$R$（所谓的哈默尔基础）。我们的构造也是密集对的扩展$\left( {; + , < ,} \right)$并且在自然语言中具有完全的量词消除。