First-order Model Theory
First-order model theory, also known as classical model theory, is a branch of mathematics that deals with the relationships between descriptions in first-order languages and the structures that satisfy these descriptions. From one point of view, this is a vibrant area of mathematical research that brings logical methods (in particular the theory of definition) to bear on deep problems of classical mathematics. From another point of view, first-order model theory is the paradigm for the rest of model theory; it is the area in which many of the broader ideas of model theory were first worked out.
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