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It must be stressed that Skolem's paradox is not a paradox in the strict sense of the word, that is, in no way does it show the inconsistency of the theory within whose limits it is established (see also Antinomy). For example, in a countable model of Zermelo–Fraenkel theory, every set is countable from an external point of view. However, in set theory the existence of uncountable sets is provable; so the model also contains sets $S$ which are uncountable from an internal point of view, in the sense that inside the model there is no enumeration of the set $S$.