Proof Theory 2014/2015: Contents

Contents of the course

• Directed systems, ultrapowers
• Compactness Theorem
• Lowenheim-Skolem theorems
• Diagrams, Los-Tarski Theorem, Chang-Los-Suszko Theorem
• Robinson's Consistency Theorem, Craig Interpolation Theorem, Beth Definability Theorem
• Types and type spaces, saturated models
• Quantifier elimination
• Examples (fields, dense linear orders, atomless boolean algebras, et cetera)
• Countable models: omitting types, omega-categoricity, prime and atomic models
• Ehrenfeucht-Fraisse games

Contents of the individual lectures

• 4 February: Basic notions

Exercise sheets

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