Model 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
• Countable models: omitting types, omega-categoricity, prime and atomic models
• Ehrenfeucht-Fraisse games
• Quantifier elimination
• Examples (fields, dense linear orders, atomless boolean algebras, random graph,...)

Contents of the individual lectures

• 4 February: Basic notions, slides for week 1 available here
• 5 February: Downward Loewenheim-Skolem, dense linear orders, directed systems
• 11 February: Compactness Theorem, diagrams, Los-Tarski Theorem, slides for week 2 available here
• 12 February: Chang-Los-Suszko Theorem, Robinson's Consistency Theorem, Craig Interpolation Theorem, Beth Definability Theorem
• 18 February: Types and type space, slides for week 3 available here
• 19 February: Omega-saturated models
• 25 February: Countable omega-saturated models, slides for week 4 available here
• 26 February: Omitting types theorem
• 4 March: Omega-categoricity, handout available here
• 5 March: Prime and atomic models
• 11 March: Quantifier elimination, handout available here
• 12 March: Quantifier elimination: examples
• 18 March: Ehrenfeucht-Fraisse games, handout available here
• 19 March: Ultrapowers, handout available here

Exercise sheets

First Exercise Sheet
Second Exercise Sheet
Third Exercise Sheet
Fourth Exercise Sheet
Fifth Exercise Sheet
Sixth Exercise Sheet
Seventh Exercise Sheet

To main page.