Hamel spaces and distal expansions

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Journal of Symbolic Logic 85 (1):422-438 (2020)
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Abstract

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

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10.1017/jsl.2019.54

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