Model Theory

The branch of mathematical logic that studies formal languages and their interpretations (models), focusing on the relationships between syntactic theories and semantic structures: satisfiability, elementary equivalence, definability, types, and model-theoretic properties such as completeness, compactness, and stability.

The branch of mathematical logic that studies formal languages, theories, and their models, connecting syntactic properties of theories (like completeness and decidability) with semantic properties of classes of structures (such as categoricity, stability, and elimination of imaginaries) and providing tools to analyze algebraic structures via logical invariants.