Ideas from 'Introduction to Zermelo's 1930 paper' by Michael Hallett [1996], by Theme Structure
[found in 'From Kant to Hilbert: sourcebook Vol. 2' (ed/tr Ewald,William) [OUP 1996,0198505361]].
Click on the Idea Number for the full details 
back to texts

expand these ideas
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17833

The firstorder ZF axiomatisation is highly noncategorical

17832

Zermelo showed that the ZF axioms in 1930 were noncategorical

17835

Gödel show that the incompleteness of set theory was a necessity

17834

Noncategoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17837

Zermelo allows urelements, to enable the widespread application of settheory

6. Mathematics / A. Nature of Mathematics / 4. The Infinite / g. Continuum Hypothesis
17836

The General Continuum Hypothesis and its negation are both consistent with ZF
