Tame extension of almost o-minimal structure

Masato Fujita

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arXiv · 2207.03021

Tame extension of almost o-minimal structure

Masato Fujita

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Abstract

We consider an almost o-minimal expansion of an ordered group $\mathcal M=(M,<,+,0,\ldots)$ and its tame extension $\mathcal N=(N,<,+,0,\ldots)$. We demonstrate that the subset $\{x \in M^n\;|\; \mathcal N \models \Phi(x,a)\}$ of $M^n$ defined by a formula $\Phi(x,y)$ with $\mathcal M$-bounded parameters $a$ in $\mathcal N$ is $\mathcal M$-definable. We also introduce its corollaries.

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BibTeX RIS

Masato Fujita. 2022-07-07. Tame extension of almost o-minimal structure. https://arxiv.org/abs/2207.03021

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