Löwenheim-Skolem theorem

The Löwenheim-Skolem theorem is a fundamental result in logic that addresses the relationship between formal languages and their models. It states that if a theory (a set of statements or axioms) can describe an infinite structure, then it can also describe structures of varying sizes—both smaller and larger—within the same framework. This means that if a system can be understood in one context, it can also be understood in many others, highlighting the flexibility and limitations of formal theories in capturing the full breadth of mathematical reality.