 A simple version of the Löwenheim-Skolem theorem states that if a set of formulas \(\Gamma\) has an infinite model, then it has a denumerable model, where a denumerable model is one whose domain is no larger than the set of natural numbers. There is a generalized form as well. If we let the cardinality \(\kappa\) of the non-logical vocabulary be greater than \(\aleph_0\), which is the cardinality of the set of natural numbers, then if \(\Gamma\) has an infinite model, then it has a model of cardinality \(\kappa\).