Introduction to Model Theory
by Philipp Rothmaler · Philipp Rothmaler
Introductory textbook on model theory for students with some algebra and logic background. Builds first-order structures, compactness, elementary extensions, quantifier elimination and types, using algebraic examples such as fields and modules, and closes with saturation, countable models and categoricity.
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plato.stanford.edu
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nLab: Model Theory
Entry in the nLab, a research-level mathematics wiki, framing model theory as the relationship between syntax and semantics. Covers first-order structures, Tarski's truth definition, the completeness, compactness and Łoś ultraproduct theorems, and categorical views via Lawvere theories, monads and accessible categories.
Stanford Encyclopedia of Philosophy: Model Theory
Stanford Encyclopedia of Philosophy entry explaining what model theory studies: how formal sentences are interpreted in mathematical structures. Covers basic notions such as definability, elementary equivalence and compactness, and the field's philosophical significance, with a substantial bibliography for further reading.
A Course in Model Theory
Graduate textbook in the Cambridge Lecture Notes in Logic series covering modern model theory from the basics through quantifier elimination, countable models, strongly minimal sets, Morley rank, and stable and simple theories. Prepares readers for research literature in stability and classification theory.
Model Theory
Classic graduate textbook on first-order model theory, reissued as a Dover third edition. Develops models built from constants, elementary chains, ultraproducts, and saturated and special models, giving readers the classical toolkit that later texts on stability theory assume.