- #1
tzimie
- 259
- 28
Reading this: https://en.wikipedia.org/wiki/List_of_large_cardinal_properties
I perfectly understand the motivation for the inaccessible cardinal, it looks very natural from the theory of ordinals, but everything beyond makes no sense to me. Why Mahlo? Why superstrong? It looks like a game "What if there is so large cardinal that it has the following weird property: <you name it>"
While "what-if" game is good for math, I fail to understand what was driving the choice of the specific weird properties in the "formula" (I stressed in italic) above. Especially reading this: https://en.wikipedia.org/wiki/Vopěnka's_principle
I perfectly understand the motivation for the inaccessible cardinal, it looks very natural from the theory of ordinals, but everything beyond makes no sense to me. Why Mahlo? Why superstrong? It looks like a game "What if there is so large cardinal that it has the following weird property: <you name it>"
While "what-if" game is good for math, I fail to understand what was driving the choice of the specific weird properties in the "formula" (I stressed in italic) above. Especially reading this: https://en.wikipedia.org/wiki/Vopěnka's_principle
Vopěnka's principle was originally intended as a joke: Vopěnka was apparently unenthusiastic about large cardinals and introduced his principle as a bogus large cardinal property, planning to show later that it was not consistent