The Löwenheim-Skolem Theorem

The Löwenheim-Skolem Theorem states that if a logical system can describe a certain structure or system with infinite elements, then it can also describe a smaller, countable version of that structure. In other words, even if a theory involves an infinite amount of information, there's always a way to find a version of it that’s countable and still captures the same properties. This highlights that the size of infinite structures in logic doesn't necessarily match their complexity, leading to interesting implications about how mathematical systems relate to their potential models.