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arXiv · 2506.21846

Connected components in d-minimal structures

Masato Fujita
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Abstract

For a given d-minimal expansion $\mathfrak R$ of the ordered real field, we consider the expansion $\mathfrak R^\natural$ of $\mathfrak R$ generated by the sets of the form $\bigcup_{S \in \mathcal C}S$, where $\mathcal C$ is a subfamily of the collection of connected components of an $\mathfrak R$-definable set. We prove that $\mathfrak R^{\natural}$ is d-minimal. A similar assertion holds for almost o-minimal expansions of ordered groups.

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Masato Fujita. 2025-06-27. Connected components in d-minimal structures. https://arxiv.org/abs/2506.21846

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