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Mathematics

Model Theory Basics: Satisfaction, Consistency, and Completeness

Quick fact

In model theory, a structure can satisfy a statement even if that statement is not provable in a formal system. For example, a countably infinite structure can satisfy statements that imply the existence of uncountable sets, a phenomenon known as Skolem's paradox.

Why this is interesting

Imagine a formal language as a set of rules for building 'sentences.' How do we decide whether those sentences are actually true? In model theory, truth is not about the world—it's about a specific structure.