Mathematical
Skolem's Paradox
Set theory proves uncountable sets exist, yet has a countable model
Overview
A paradox showing that set theory can prove uncountable sets exist within a countable model.
Zermelo-Fraenkel set theory proves real numbers are uncountable. But by the Löwenheim-Skolem theorem, ZF has a countable model. So there's a model where 'uncountable' sets exist, but the model itself is countable. How can uncountable sets exist in a countable model?