Hello,

I looked through MathOverflow's existing entries but couldn't find a satisfactory answer to the following question:

What is the relationship between **No**, Conway's class of surreal numbers, and **V**, the Von Neumann set-theoretical universe?

In particular, does **V** contain all the surreal numbers? If so, then is there a characterization of the surreal numbers as sets in **V**? And does **No** contain large cardinals?

I came across surreal numbers recently, but was surprised by the seeming lack of discussion of their relationship to traditional set theory. If they are a subclass of **V**, then I suppose that could explain why so few people are studying them.

Thank you,
Alex