Skolem's paradox
= Skolem's paradox
{c}
A <countable> model of <set theory> can internally assert that an <uncountable> set exists. There is no contradiction because “there is a <bijection>” ranges only over functions in the model. An external enumeration of its domain need not itself be an element of that domain. <Löwenheim-Skolem theorem> controls external <cardinality>; <Cantor's theorem> remains valid for the sets and functions that the model contains.