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What name does this "well-developed field of mathematics" go by? (I just want to get a taste of what the field is like.) I also thought that there are an infin
by kdavis 26d ago
What name does this "well-developed field of mathematics" go by? (I just want to get a taste of what the field is like.)
I also thought that there are an infinite set of possible extra axioms, e.g. axiomize any statement that's true but not provably so via Gödel's First Incompleteness Theorem, though maybe the vast majority of such axioms are "uninteresting".
- QuesnayJr 26d ago"Descriptive set theory" is a good starting point, though it's the bulk of what set theorists in general do. It's true that there's an infinite possible set of axioms. It does seem that the types of axioms that have consequences that humans are interested in fall into simple families. For example, many seemingly unrelated questions are settled by assume the existence of very large sets (larger than can normally constructed in set theory).