1996 | Introduction to Zermelo's 1930 paper |
p.1209 | p.1209 | 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical |
p.1213 | p.1213 | 17833 | The first-order ZF axiomatisation is highly non-categorical |
p.1215 | p.1215 | 17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal |
p.1215 | p.1215 | 17835 | Gödel show that the incompleteness of set theory was a necessity |
p.1217 | p.1217 | 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory |
p.1217 | p.1217 | 17836 | The General Continuum Hypothesis and its negation are both consistent with ZF |