Ideas of Michael Hallett, by Theme

[British, fl. 1996, Professor at McGill University, Montreal.]

idea number gives 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
The first-order ZF axiomatisation is highly non-categorical
Zermelo showed that the ZF axioms in 1930 were non-categorical
Gödel show that the incompleteness of set theory was a necessity
Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Zermelo allows ur-elements, to enable the widespread application of set-theory
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / g. Continuum Hypothesis
The General Continuum Hypothesis and its negation are both consistent with ZF