ABSTRACT
Any countable, consistent, first-order theory has a countable model. Moreover, given any uncountable model of such a theory, a countable model may be extracted from it. This is one version of the Löwenheim-Skolem theorem. It’s sensitive to the resources of the underlying logic, vanishing if we go second-order, modify quantificational power, or alter the upper cardinal boundary on sentence length. But it’s a deep result for all that, since such modifications can be costly.1
