7 ideas
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
7803 | Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle] |