In this paper by Jeff Ketland, he notes: With Henkin semantics, the Completeness, Compactness and Löwenheim-Skolem Theorems all hold, because Henkin structures can be re-interpreted as many-sorted ...
In relation to this question about the "fundamental" character of possible logical systems, I realized that I just had an intuitive (and so, inadequate) understanding of the way logics higher than FOL ...
As I look over the post that has the similar question, I began to wonder: The only reason I found is that first-order logic can prove validity of some second-order logic formula/sentences, as some of ...
There are statements $\varphi$ that are independent of first-order Peano Axioms. Are these statements also independent of second-order Peano Axioms? I'm reading Wikipedia articles around ...