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Model theory is the branch of mathematical logic that deals with the relationship between a formal language and its interpretations, or models. It studies the properties of these models and the relationships between them, with a focus on understanding the implications of sentences and theories in the language on the structures they define. Model theory is concerned with questions of existence, classification, and categorization of mathematical structures based on these interpretations. It also investigates the behaviors and properties of different classes of structures, as well as the properties and limitations of formal languages themselves.