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
Canonical name	DownwardLowenheimSkolemTheorem
Date of creation	2013-03-22 13:00:42
Last modified on	2013-03-22 13:00:42
Owner	Evandar (27)
Last modified by	Evandar (27)
Numerical id	5
Author	Evandar (27)
Entry type	Theorem
Classification	msc 03C07