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.