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arXiv · 2205.04199

Additive reducts of real closed fields and strongly bounded structures

Hind Abu Saleh·Ya'acov Peterzil
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Abstract

Given a real closed field $R$, we identify exactly four proper reducts of $R$ which expand the underlying (unordered) $R$-vector space structure. Towards this theorem we introduce a new notion, of strongly bounded reducts of linearly ordered structures: A reduct $\mathcal M$ of a linearly ordered structure $\langle R;<,\cdots\rangle $ is called \emph{strongly bounded} if every $\mathcal M$-definable subset of $R$ is either bounded or co-bounded in $R$. We investigate strongly bounded additive reducts of o-minimal structures and as a corollary prove the above theorem on additive reducts of real closed fields.

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BibTeXRIS

Hind Abu Saleh, Ya'acov Peterzil. 2022-05-09. Additive reducts of real closed fields and strongly bounded structures. https://doi.org/10.2140/mt.2023.2.381

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