An Introduction to Good Old Fashioned Model Theory
by Harold Simmons
Publisher: The University of Manchester 2004
Number of pages: 180
Following topics are covered: Basic ideas of language, satisfaction, and compactness; Some examples of elimination of quantifiers; The diagram technique; Model complete theories, companion theories, existentially closed structures, and various refinements; Atomic structures and sufficiently saturated structures; The splitting technique and N0-categoricity.
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by Jan Wolenski - ESSLLI
This text provides the basic information about the metatheory of formal system. It will start with a brief information about propositional calculus and first-order logic. Then, fundamental theorems about elementary logic will be stated and proved.
by D. Haskell, A. Pillay, C. Steinhorn - Cambridge University Press
The book gives the necessary background for the model theory and the mathematics behind the applications. Aimed at graduate students and researchers, it contains surveys by leading experts covering the whole spectrum of contemporary model theory.
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The subject matter of this book constitutes a merging of several directions in general model theory: cardinality quantifiers; infinitary languages; and, finally, that on generalized quantifiers and abstract characterizations of first-order logic.
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An important branch of mathematical logic is model theory, the study of first-order theories and the classes of models defined by such theories. This course will include numerous applications of model theory to algebra, especially ordered fields ...