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TOC
Chapt 0.
Models, Truth and Satisfaction
Formulas, Sentences, Theories and Axioms
Prenex Normal Form
Chapt 1.
Notation and Examples
Chapt 2.
Compactness and Elementary Submodels
Compactness Theorem
Isomorphisms, elementary equivalence and complete theories
Elementary Chain Theorem
Loowenheim-Skolem Theorems
The Los-Vaught Test
Every complex onetoone polynomial map is onto
Chapt 3.
Diagrams and Embeddings
Diagram Lemmas
Every planar graph can be four coloured
Ramsey’s Theorem
The Leibniz Principle and infinitesimals
Robinson Consistency Theorem
Craig Interpolation Theorem
Chapt 4.
Model Completeness
Robinson’s Theorem on existentially complete theories
Lindstroom’s Test
Hilbert’s Nullstellensatz
Chapt 5.
The Seventeenth Problem
Positive definite rational functions are the sums of squares
Chapter 6. Submodel Completeness
Elimination of quantifiers
The Tarski-Seidenberg Theorem
Chapt 7.
Model Completions
Almost universal theories
Saturated models
Blum’s Test
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