Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Fujita, Masato
Institutions: World Education Services, Japan Coast Guard Academy
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416260452
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