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Just curious as to wether the Lowenheim-Skolem theorem is constructive , in the sense

that , while it guarantees the existence of a model of infinite cardinality -- given the

existence of any infinite model -- does it give a prescription for constructing them?

I was thinking mostly of the ( 1st order theory of) the reals: the standard model is

the one given in most books. Then we can construct the hyperreals using, e.g.,

ultraproducts. What if we had any other infinite cardinal κ : is there a method for

constructing a model of cardinality κ ?

Thanks.

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# Lowenheim-Skolem and Constructive

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