# 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 UpwardLowenheimSkolemTheorem 2013-03-22 13:00:39 2013-03-22 13:00:39 Evandar (27) Evandar (27) 6 Evandar (27) Theorem msc 03C07