Re:A New Bridge Links the Math of Infinity to Computer Science
by zozbot234 on Wednesday November 26, 2025 @08:32AM
(#46057237)
The standard semantics for second-order logic are not very practical and arguably not even all that meaningful or logical (as argued e.g. by Willard Quine); you can use Henkin semantics (i.e. essentially a many-sorted first-order theory) to recover the model-theoretic properties of first-order logic, including Löwenheim-Skolem.
Ernst Zermelo resolved this by stating that his axioms should be interpreted within second-order logic, and as such it doesn't contradict Cantor's theorem since the Löwenheim–Skolem theorem only applies in first-order logic.