If there's an infinite model of some first-order logical system, then there's a model of the same logical system of any infinite cardinality. [1] Thus, there e

If there's an infinite model of some first-order logical system, then there's a model of the same logical system of any infinite cardinality. [1] Thus, there exists countable model of reals, as well as models of greater-than-continuum cardinalities. [1] http://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem http://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_t...