Hi, 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.