PlanetMath: downward Lowenheim-Skolem theorem

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downward Lowenheim-Skolem theorem

(Theorem)

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

"downward Lowenheim-Skolem theorem" is owned by Evandar. [ full author list (2) ]

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Cross-references: first order language
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This is version 2 of downward Lowenheim-Skolem theorem, born on 2002-08-29, modified 2008-06-09.
Object id is 3394, canonical name is DownwardLowenheimSkolemTheorem.
Accessed 3035 times total.

Classification:

AMS MSC:

03C07 (Mathematical logic and foundations :: Model theory :: Basic properties of first-order languages and structures)

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