5.2 Lowenheim Skolem
The Lowenheim Skolem theorems describe how the size of models of a first order theory can be changed without affecting truth of sentences, and they show that if a theory has any infinite model, then it has models of many different infinite sizes, which reveals an important limitation of first order logic in controlling cardinality. Definition 5.10 (Cardinality of a Structure) Let $\mathcal{M}$ be a structure with underlying set $M$....