4 ms·
Infinite sets are a useful abstraction, but uncountable infinities can probably be avoided since the Löwenheim-Skolem[0] theorem says that any countable first-o
by cuspycode 6y ago
Infinite sets are a useful abstraction, but uncountable infinities can probably be avoided since the Löwenheim-Skolem[0] theorem says that any countable first-order theory has a countable model.
[0] https://en.wikipedia.org/wiki/Löwenheim-Skolem_theorem https://en.wikipedia.org/wiki/Löwenheim-Skolem_theorem
- ukj 6y agoLöwenheim-Skolem doesn't hold for higher order logics such as type theory/Lambda calculus. Basically, it doesn't hold for any constructive logic.