9 ideas
23367 | Even pointing a finger should only be done for a reason [Epictetus] |
17879 | Axiomatising set theory makes it all relative [Skolem] |
17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |