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Suppose $N$ is elementarily equivalent to an archimedean ordered abelian group $(G,+,<)$ with small quotients (for all $1 \leq n < \omega$, $[G: nG]$ is finite). Then every stable reduct of $N$ which expands $(G,+)$ (equivalently every reduct that do
Externí odkaz:
http://arxiv.org/abs/2412.10336
Autor:
Alouf, Eran
We first prove that if $\mathcal{Z}$ is a dp-minimal expansion of $\left(\mathbb{Z},+,0,1\right)$ which is not interdefinable with $\left(\mathbb{Z},+,0,1,<\right)$, then every infinite subset of $\mathbb{Z}$ definable in $\mathcal{Z}$ is generic in
Externí odkaz:
http://arxiv.org/abs/2402.11146
Autor:
Alouf, Eran
We show that if $ \mathcal{Z} $ is a dp-minimal expansion of $ \left(\mathbb{Z},+,0,1\right) $ that defines an infinite subset of $ \mathbb{N} $, then $ \mathcal{Z} $ is interdefinable with $ \left(\mathbb{Z},+,0,1, < \right) $. As a corollary, we sh
Externí odkaz:
http://arxiv.org/abs/2001.11480
Autor:
Alouf, Eran, d'Elbée, Christian
Publikováno v:
J. symb. log. 84 (2019) 632-663
We consider the structure $(\mathbb{Z},+,0,|_{p_{1}},\dots,|_{p_{n}})$, where $x|_{p}y$ means $v_{p}(x)\leq v_{p}(y)$ and $v_p$ is the $p$-adic valuation. We prove that its theory has quantifier elimination in the language $\{+,-,0,1,(D_{m})_{m\geq1}
Externí odkaz:
http://arxiv.org/abs/1707.07203
Autor:
ALOUF, ERAN, D’ELBÉE, CHRISTIAN
Publikováno v:
The Journal of Symbolic Logic, 2019 Jun 01. 84(2), 632-663.
Externí odkaz:
https://www.jstor.org/stable/26788466
