Model Theory 2011/2012: Contents of classes
Lectures
- May 23: Lindström's Theorem
Material: Jouko Väänänen's slides
- May 16: omega-categoricity.
Material: Hodges Chapter 6: 3,4.
- May 09: omitting types, automorphisms.
Material: Hodges Chapter 6: 2; Chapter 4: 1.
- May 02: saturation, Fraisse construction.
Material: Hodges Chapter 8: 1; Chapter 6: 1.
- Apr 25: regular ultraproducts, saturation.
Material: Hodges Chapter 8: 5,1.
- Apr 18: no class.
- Apr 11: Ultraproducts
Material: Hodges Chapter 8: 5.
- Apr 04: Amalgamation and preservation
Material: Hodges Chapter 5: 4-5.
- Mar 28: no class.
- Mar 21: Amalgamation and preservation
Material: Hodges Chapter 5: 3-4.
- Mar 14: Types; elementary amalgamation
Material: Hodges Chapter 5: 2-3.
- Mar 07: Games of finite length
Material: Hodges Chapter 3: 3.
- Feb 29: Loewenheim-Skolem theorem; Ehrenfeucht-Fraisse games.
Material: Hodges Chapter 3: 1-2.
- Feb 22: preservation; quantifier elimination.
Material: Hodges Chapter 2: 4,5,7.
- Feb 15: Logical notions; Hintikka sets; compactness
Material: Hodges Chapter 2: 3; Chapter 5: 1.
- Feb 09: Diagrams; canonical models; languages; models and
theories.
Material: Hodges Chapter 1: 4-5; Chapter 2: 1-2.
- Feb 08: Introduction.
Material: Hodges Chapter 1: 1-3.
Exercise sessions
- May 24: Hodges 6.3.1, 6.3.2, 6.3.3,
Material: Väänänen's
Problems 5, 6.
- May 17: no class
- May 10: Exercises 6.2.3, 6.2.4, 6.2.7.
- May 03: Prove Lemma 6.1.5.
Exercise 6.1.1, 6.1.4.
- Apr 26: Exercise 8.5.3, 8.5.9.
Show that if \alpha is bigger than the size of the language,
then \alpha-homogeneity and \alpha-universality together imply
\alpha-saturation.
- Apr 19: Prove Thm 8.5.3; Exercise 8.5.1, 8.5.2, 8.5.5.
- Apr 12: no class.
- Apr 05: Exercises 5.4.2, 5.5.1, 5.5.7.
- Mar 29: no class.
- Mar 22: Exercises 5.2.1, 5.2.6, 5.3.2, 5.3.4, 5.3.6.
- Mar 15: Exercises 3.3.1, 3.3.5, 3.3.7, 3.3.9.
- Mar 08: Exercises 3.1.5, 3.1.7, 3.2.4, 3.2.5, 3.2.2.
- Mar 01: Exercises 2.4.4, 2.5.1, 2.5.5, 2.5.2, 2.7.2, 2.7.3.
- Feb 23: Exercises 2.3.3, 2.3.8, 5.1.1, 5.1.5, 5.1.7.
- Feb 16: Exercises 1.2.3, 1.2.6, 1.5.2, 2.1.8, 2.2.1.
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