Ideas of Michael Hallett, by Theme
[British, fl. 1996, Professor at McGill University, Montreal.]
green numbers give full details 
back to list of philosophers 
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

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 / 5. The Infinite / g. Continuum Hypothesis
17836

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