upward Lowenheim-Skolem theorem

Let $L$ be a first-order language and let $\mathcal{A}$ be an infinite $L$ -structure. Then if $\kappa$ is a cardinal with $\kappa\geq\operatorname{Max}(\lvert\mathcal{A}\rvert,\lvert L\rvert)$ then there is an $L$ -structure $\mathcal{B}$ such that $\lvert\mathcal{B}\rvert=\kappa$ and $\mathcal{A}\preccurlyeq\mathcal{B}$ .

Title	upward Lowenheim-Skolem theorem
Canonical name	UpwardLowenheimSkolemTheorem
Date of creation	2013-03-22 13:00:39
Last modified on	2013-03-22 13:00:39
Owner	Evandar (27)
Last modified by	Evandar (27)
Numerical id	6
Author	Evandar (27)
Entry type	Theorem
Classification	msc 03C07