SUGGESTED SYLLABUS - MATH 282 A-B-C

Model Theory

Possible textbooks for the first two quarters are "Model-Theory" by C. Chang and H. Keisler or "Model Theory" by W. Hodges. For the last quarter: ≥An introduction to stability theory" by A. Pillay or " Model Theory" by B. Poizat.

Quarter 1

Review of languages, models, satisfaction

Theories and examples of theories.

Elementary equivalence. The back-and-forth method.

Elementary extensions and elementary chains.

Completeness and compactness.

Lowenheim-Skolem Theorems.

Omitting and Interpolation theorems.

Interpretations.

Direct products, reduced products and ultraproducts.

Countable models of complete theories.

Quarter 2

Saturated and special models.

Indiscernibles.

Categorical theories.

Existentially closed structures.

Model-companions and model-completions.

Quantifier elimination.

Decidable theories.

Applications to algebra: Boolean algebras, fields, abelian groups, modules.

0-minimality.

Quarter 3

Definable types.

Stability and order.

Forking.

Ranks.

Stability.

Morley and Baldwin-Lachlan theorems.

Further topics in classification theories.