The surreal complex field $\text{No}[i]$, known as the [surcomplex field](https://en.wikipedia.org/wiki/Surreal_number#Surcomplex_numbers), is a proper-class-sized set-saturated algebraically closed field. It is universal for all fields of characteristic 0. Indeed, under global choice, every class field structure in characteristic 0 embeds as a subfield of $\text{No}[i]$.