Math 506 Model Theory I
Spring 2011
- REVIEW Read Chapter 1
- Week 1 The Compactness Theorem, Henkin constructions
Read Chapter 2.1
- Week 2 embeddings, elementary equivalence, preservation of quantifier free formulas
under substructure, isomorphism, categorical theories
Read Chapter 2.2
- Week 3 Vaught's Test, transfer theorems for algebraically closed fields,
Ax's Theorem,
dense linear orders, elementary embeddings, method of diagrams,
Read Chapter 2.3 and 2.4 48-52
- Week 4
Skolem functions and the Lowenheim-Skolem Theorem, elementary chains, characterization of universal axiomatizability and
formulas equivalent to universal formulas,
Read Chapter 2.3
- Week 5 quantifier elimination tests, QE in dense linear orders, divisible abelian groups,
Read Chapter 3.1 (up to pg 81)
- Week 6 quantifier elimination in divisible ordered abelian groups.
quantifier elimination in algebraically closed fields and applications,
Read Chapter 3.2 (up to pg 91)
- Week 7 real closed fields
Read Chapter 3.3 (up to pg 101)
- Week 8 types, Stone topology on type spaces, types in algebraically closed fields,
omitting types theorem
Read Chapter 4.1, 4.2 125-127\
- Week 9 Prime models, atomic models, countable homogeneous models
Read Chapter 4.2 129-135
- Week 10 countable saturated models, existence of saturated models, homogenous-universal models
Read Chapter 4.3: 138-145
- Spring Break
- Week 11 applications of saturated models, aleph_0-categorical theories, the number of countable models
Read Chapter 4.3: 146-147, Chapter 4.4: 155-158
- Week 12 omega-stable theories, prime-model extensions, Ramsey's Theorem
Read Chapter 4.2:135-138, Chapter 5.1: 175-177
- Week 13 order indiscernibles, Ehrenfeucht-Mostowski models, stretching indiscernibles, uncountably categorical
theories are omega-stable
Read Chapter 5.2:178-183
- Week 14 indiscernibles in stable theories, Vaught's two-cardinal theorem, two cardinal theorem for omega-stable
theories
Read Chapter 5.2: 184-185, Chapter 4.3: 151-155
- Week 15 strongly minimal sets, existence of strongly minimal formulas, Morley's Theorem
Read Chapter 6.1: 207-215
Last revised: 2/28/11