One of the great theorems in logic is the Lowenheim-Skolem theorem [1], which says that if a countable first-order model has an infinite model, then there is a

One of the great theorems in logic is the Lowenheim-Skolem theorem [1], which says that if a countable first-order model has an infinite model, then there is a countably infinite model. For example, there is a countably infinite model for the theory of reals. I have heard that Skolem [2] used this theorem as a basis for his belief that uncountable sets can be avoided, and countably infinite sets suffice. [1] https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_... [2] http://www-gap.dcs.st-and.ac.uk/history/Biographies/Skolem.html http://www-gap.dcs.st-and.ac.uk/history/Biographies/Skolem.h...