Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamel Spaces and Distal Expansions   In this note, we construct a distal expansion for the structure $(\mathbb{R};
+,<,H)$, where $H\subseteq \mathbb{R}$ is a dense $\mathbb{Q}$-vector space
basis of $\mathbb{R}$ (a so-called Hamel basis). Our construction is also an
expansion of the dense pair $(\mathbb{R}; +,<,\mathbb{Q})$ and has full
quantifier elimination in a natural language.

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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph