This is a question in two parts about the interaction of surreal numbers and large cardinals, in both cases just a request for references on the subject. Part 1 is about foundations. Much of the ...
In an attempt to understand a bit better large cardinals, I have been thinking along the following lines, which could be summarized under the slogan Talk about cardinals without the (ambient) ...
Cantor has, in the immortal words of D. Hilbert, given all of us a paradise (or perhaps, I would rather say, a great vacation spot), the TRANSFINITE. $\aleph_0, \aleph_1,\aleph_2\dots$ the lists ...