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