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