Post #2668010
2026-05-07 17:17 UTC
@mc@mathstodon.xyz I want to ask, who is the customer for this product.
“Core” mathematicians should be able to ignore foundations, and I assume they mostly do.
Set theorists are fine, thanks.
For non-set theorists interested in foundations, a set that includes me, the literature shows lots of ways to mix and match axioms if e.g. you don’t like arbitrary choice, or if Replacement gives you a bad vibe.
I do see some value in narrowing the gap between math-as-encoded (in a foundational system) and math-as-practiced, but that’s not what’s happening here, AFAICT.
Replies (1)
-
@highergeometer@mathstodon.xyz 2026-05-08 00:01
@cdrichards@mathstodon.xyz Since Sy-David Friedman is a hardcore set theorist, of course he's going to use Collection, rather than realise that it's wholly unnecessary for the purposes they are aiming for. I would say to people who think that ETCS is a bit too weak (no Borel Determinacy!), then add the structural axiom 'all beths exist' that Tom introduced later: https://golem.ph.utexas.edu/category/2021/06/large_sets_6.html But since the Mumford–Friedman approach is to eschew power sets, then they are really doing something like wanting to work in a well-pointed Boolean pretopos with indexed NNO plus a real number object or something. @mc@mathstodon.xyz