# downward Lowenheim-Skolem theorem

Let $L$ be a first order language, let $\mathcal{A}$ be an $L$-structure and let $K\subseteq\operatorname{dom}(\mathcal{A})$. Then there is an $L$-structure $\mathcal{B}$ such that $K\subseteq\mathcal{B}$ and $|\mathcal{B}|\leq\operatorname{Max}(|K|,|L|)$ and $\mathcal{B}$ is elementarily embedded in $\mathcal{A}$.

Title downward Lowenheim-Skolem theorem DownwardLowenheimSkolemTheorem 2013-03-22 13:00:42 2013-03-22 13:00:42 Evandar (27) Evandar (27) 5 Evandar (27) Theorem msc 03C07