You might already know about it, but Ehrlich claims[1] that the Surreals form an ordered field which is a maximal hyperreal number system in NBG, and therefore

You might already know about it, but Ehrlich claims[1] that the Surreals form an ordered field which is a maximal hyperreal number system in NBG, and therefore all the results of non-standard analysis "work" (up to isomorphism) in the Surreals. [1] Philip Ehrlich. "The absolute arithmetic continuum and the unification of all numbers great and small." Bull. Symbolic Logic 18 (1) 1 - 45, March 2012. https://doi.org/10.2178/bsl/1327328438 https://doi.org/10.2178/bsl/1327328438 Theorem 20