The hyperreals and surreals are actually isomorphic under a mild strengthening of the axiom of choice (NBG). https://mathoverflow.net/questions/91646/surreal-n

The hyperreals and surreals are actually isomorphic under a mild strengthening of the axiom of choice (NBG). https://mathoverflow.net/questions/91646/surreal-numbers-vs-non-standard-analysis/91654#91654 https://mathoverflow.net/questions/91646/surreal-numbers-vs-... See Ehrlich’s answer.