summer 2010

2010 Summer Course on Model Theory Pete

Introduction 1 0.1. Some theorems in mathematics with snappy model-theoretic proofs 1 1. Languages, structures, sentences and theories 1 1.1. Languages 1 1.2. Statements and Formulas 4 1.3. Satisfaction 5 1.4. Elementary equivalence 6 1.5. Theories 7 2. Big Theorems: Completeness, Compactness and Löwenheim-Skolem 9 2.1. The Completeness Theorem 9 2.2. Proof-theoretic consequences of the complet...

2010 Summer Course on Model Theory

Introduction 2 0.1. Some theorems in mathematics with snappy model-theoretic proofs 2 1. Languages, structures, sentences and theories 2 1.1. Languages 2 1.2. Statements and Formulas 5 1.3. Satisfaction 6 1.4. Elementary equivalence 7 1.5. Theories 8 2. Big Theorems: Completeness, Compactness and Löwenheim-Skolem 9 2.1. The Completeness Theorem 9 2.2. Proof-theoretic consequences of the complet...

full journal+appendix (summer 2010)

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Summer 2010 Course on Model Theory : Chapter 5

Having seen that categoricity is a concept of somewhat limited usefulness, we now turn to a more versatile (and historically prior) technique for establishing model completeness, namely quantifier elimination. But more than just giving further criteria for showing that theories are model / completen, quantifier elimination is a fundamental concept in its own right (arguably more so than categor...

Summer 2010 Course on Model Theory: Chapter 4

By Löwenheim-Skolem, any theory in a countable language which admits infinite models admits models of every infinite cardinality, and indeed, models of any given cardinality elementarily equivalent to any fixed infinite model. Thus the next step in understanding the relation of elementary e equivalence is to consider models of a fixed cardinality. In this regard, the following definition captur...

Summer 2010 Course on Model Theory and Its Applications