sentences:  The paradox can be resolved by noting that countability is not absolute to submodels of a particular model of ZFC.It is possible that a set "X" is countable in a model of set theory but uncountable in a submodel containing "X", because the submodel may contain no bijection between "X" and ω, while the definition of countability is the existence of such a bijection.The Löwenheim–Skolem theorem, when applied to ZFC, shows that this situation does occur.