Math 506 Model Theory
Fall 2008
- REVIEW Read Chapter 1 and Chapter 2.1
- Week 1 elementary embeddings, method of diagrams,
Skolem functions and the Lowenheim-Skolem
Read Chapter 2.3
- Week 2 categorical theories, Vaught's Test, transfer theorems for algebraically closed fields,
Ax's Theorem
Read Chapter 2.3
- Week 3 Quantifier elimination test, divisible torsion free abelian groups, dense linear orders
Read Chapter 3.1 pg 71-81 Chapter 3.2 pg 84-89
- Week 4 Quantifier elimination for ordered divisible abelian groups and algebraically closed fields
with applications. Types.
Read Chapter 3.2 pg 84-89, Chapter 4.1
- Week 5 Stone topology on type spaces, types in DLO and ACF, omitting types theorem
Read Chapter 4.2 125-128
- Week 6 Prime models, atomic models, countable homogeneous models
Read Chapter 4.2 129-135
- Week 7 countable saturated models, existence of saturated models, homogenous-universal models
Read Chapter 4.3: 138-145
- Week 8 applications of saturate models, aleph_0-categorical theories, the number of countable models
Read Chapter 4.3: 146-147, Chapter 4.4: 155-158
- Week 9 omega-stable theories, prime-model extenstions, Ramsey's Theorem
Read Chapter 4.2:135-138, Chapter 5.1: 175-177
- Week 10 order indiscernibles, Ehrenfeucht-Mostowski models, stretching indiscernibles,
Read Chapter 5.2:178-183
- Week 11 indiscernibles in stable theories, two-cardinal theorems
Read Chapter 5.2: 184-185, Chapter 4.3: 151-155
- Week 12 strongly minimal sets, existence of strongly minimal forumlas
Read Chapter 6.1: 207-213
- Week 13 Morely's categoricity theorem,
Read Chapter 6.1: 213-215
- Weeks 13-15 Morely rank, forking and independence in omega-stable theories
Read Chapters 6.2,6.3
Last revised: 10/3/08