Introduction to Model Theory

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Focusing on the model theory of first-order logic, this text presents a clear introduction that emphasizes algebraic applications, including Malcev's local theorems and Hilbert's Nullstellensatz, derived from the compactness theorem using the ultraproduct technique. It also discusses Steinitz dimension theory within a broader model-theoretic framework of strongly minimal theories. The concluding chapter delves into the models of the first-order theory of integers viewed as an abelian group, providing a comprehensive exploration of these mathematical structures.