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arXiv · 1811.12603

Hamel Spaces and Distal Expansions

Allen Gehret·Travis Nell
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Abstract

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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Allen Gehret, Travis Nell. 2018-11-30. Hamel Spaces and Distal Expansions. https://doi.org/10.1017/jsl.2019.54

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