11 ideas
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
16643 | Accidents always remain suited to a subject [Bonaventura] |
16696 | Successive things reduce to permanent things [Bonaventura] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |