/sci/ - Science & Math

So inside your subject area, you only have relatively weak tools to prove
facts, not the entire power of set theory
if new facts of set theory are required when extending the subject area,
then those facts can be established inside set theory as consequences of
ZFC, then taken as new axioms for a new version of formal axiomatic
mathematics corresponding to new theorems in your subject area
In fact, this question generally, "How has your subject area of math made
use of facts of pure set theory lately?" could be used as the basis for
a mathematical newsletter on the topic of new developments in a subject
area you study
The objective is classification and converting subject areas of math into
"formal silos" that each rely on taking various statements among
- AC1<->AC2 where AC1 and AC2 are two equivalents of AC in ZF
- a statement of "pure set theory" relying on AR
as axioms, in other words specializing ZFC to various subjects of math by
removing axioms that give information about the "internal structure" of
sets and forcing the theorems to rely on axioms that obey a discipline of
data abstraction specialized, specific, and particualr to that subject
[1] see "EYE" document at https://imgur.com/a/Gzp2Ile