Intermediate · a field of logic
Set Theory & Foundations
The ZF axioms, cardinality, and the great independence results: the standard foundation on which mathematics is built.
An entry point for mathematics
- The problem
- Is there a single consistent foundation from which all of mathematics can be built, and how large is the infinite?
- The turning point
- Cantor’s theorem says the power set is always strictly larger; the ZF axiomatization then tamed the paradoxes.
- An open question
- The continuum hypothesis is independent of ZFC, so which new axioms, if any, decide the size of the continuum?
The Canon
- Investigations in the Foundations of Set Theory 1908
- Set Theory: An Introduction to Independence Proofs
To study it
- Naive Set Theory
- Introduction to Set Theory
- The Joy of Sets