The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large…
A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…
A fundamental theorem in mathematical logic stating that any countable theory with an infinite model has models of all infinite…
The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…