Model Theory 2015/2016: Contents

Contents of the course

• Compactness Theorem
• Lowenheim-Skolem theorems
• Diagrams, Los-Tarski Theorem, Chang-Los-Suszko Theorem
• Ehrenfeucht-Fraisse games
• Directed systems
• Types and type spaces, saturated models
• Countable models: omitting types, omega-categoricity, prime and atomic models
• Quantifier elimination
• Indiscernibles, stability, Morley rank
• Morley's Theorem

Contents of the individual lectures

• 8 February: Basic definitions. Chapter 1 from this handout. In the exercise class we discussed exercises 2 and 4.
• 15 February: Diagrams, Los-Tarski Theorem, Tarski-Vaught Test. See Chapter 3 from this handout. In the exercise class we discussed exercises 1 and 2 from this handout and I gave a hint for exercise 3.
• 22 February: Compactness Theorem, Lowenheim-Skolem Theorems, categoricity, Vaught's Test. Chapter 2, Section 3.3, and Section 4.1 from handout. In the exercise class we discussed exercise 1 and 5-7 from the first handout.
• 29 February: Back-and-forth and Ehrenfeucht-Fraisse games. Sections 4.2 and 4.3 and Chapter 5 from this handout. In the exercise class we discussed exercises 2 and 3 from Chapter 4 and (briefly) exercise 1 from Chapter 5.
• 7 March: Colimits of directed systems and Craig interpolation. Chapter 6 from this handout. In the exercise class we discussed exercise 1 from this handout.
• 14 March: types and type spaces. Chapter 7 from this handout. In the exercise class we discussed exercises 1-3 from this handout.
• 21 March: isolated types and omitting types theorem. Chapter 8 from this handout. In the exercise class we discussed exercises 9 and 10 from this handout.
• 4 April: atomic and prime models, omega-categoricity. Chapter 9 from this handout. In the exercise class we discussed exercises 1 and 3 from this handout.
• 11 April: kappa-saturated models and quantifier elimination. Chapter 10 from this handout. In the exercise class we discussed exercises 1 and 2 from this handout.
• 18 April: saturated models and small theories. Chapter 11 from this handout. In the exercise class we discussed exercise 1 from this handout.
• 25 April: totally transcendental and stable theories. Theorem 3.3 and Chapter 4 from this handout. In the exercise class we discussed exercises 3-6 from this handout.
• 2 May: Morley rank and Morley degree. Chapter 5 till Lemma 5.12 from handout. In the exercise class we discussed exercises 10 and 11 from this handout.
• 9 May: Indiscernibles. Chapter 2 till Corollary 2.6 and Chapter 5 till Theorem 5.14 from handout. In the exercise class we discussed exercise 18 from this handout.
• 23 May: Morley's Theorem. We finished the handout.

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