Löwenheim's theorem

Löwenheim's theorem in logic states that if a complex set of logical statements (a theory) can be satisfied or made true in a sufficiently large structure or universe, then it can also be satisfied in a smaller, countable structure—that is, one with as many objects as there are natural numbers. In essence, if a theory is consistent and has a model, it has a "smaller" version of that model, ensuring that complex theories can often be understood or analyzed within simpler, more manageable frameworks.