PlanetMath: upward Lowenheim-Skolem theorem

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upward Lowenheim-Skolem theorem

(Theorem)

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

"upward Lowenheim-Skolem theorem" is owned by Evandar.

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Cross-references: cardinal, infinite, first-order language
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This is version 3 of upward Lowenheim-Skolem theorem, born on 2002-08-29, modified 2004-02-09.
Object id is 3393, canonical name is UpwardLowenheimSkolemTheorem.
Accessed 3325 times total.

Classification:

AMS MSC:

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

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