All Questions
4 questions
19
votes
3
answers
1k
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Large categories vs. $\mathrm{U}$-categories: why is the loss of category-theoretic information inessential?
I've asked a related question about nine months ago here, however, apparently, I lacked expertise to ask the precise question I want to ask here, as I wish to revisit the matter of universes. I hope ...
7
votes
9
answers
7k
views
Ultrainfinitism, or a step beyond the transfinite
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 ...
6
votes
1
answer
2k
views
Surreal numbers and large cardinals
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 ...
5
votes
2
answers
1k
views
Large cardinals without the ambient set theory?
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) ...