Model Theory: Third Edition

Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods — including classification theory and nonstandard analysis — the third edition added entirely new sections, exercises, and references.
Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Skolem functions, indiscernibles, ultraproducts, and special models. The final chapters present more advanced topics that feature a combination of several methods. This classic treatment covers most aspects of first-order model theory and many of its applications to algebra and set theory.

H. Jerome Keisler was a longtime professor at the University of Wisconsin, Madison, whose research included model theory and nonstandard analysis. He is known for extending the Henkin construction to what are now called Henkin-Keisler models.
C. C. Chang, Professor Emeritus of Mathematics at UCLA, also focused on model theory and proved the ordinal partition theorem. Chang's conjecture is named after him, as is ccc forcing.