Introduction to Model Theory

This course will cover a number of fundamentals of model theory including:

• Quantifer Elimination
• Applications to algebra including algebraically closed fields and real closed fields.
• Types and saturated models.

Given time, the course may also touch upon the following topics:

• Vaught’s conjecture and Morley’s analysis of countable models
• $\omega$-stable theories and Morley rank
• Fraisse’s amalgamation theorem.

Prerequisites

Students should be familiar with the following concepts: Languages, structures, formulas, theories, Godel’s completeness theorem and the compactness theorem.

We will present some basic notions and constructions from model theory, motivated by concrete questions about structures and their theories. Notions we expect to cover include:

• Types and spaces of types
• Homogeneous and saturated models
• Quantifier elimination and model companions
• Elimination of imaginaries
• Definable groups and fields

Prerequisites

Students should be familiar with the following concepts from logic: Languages, structures, formulas, theories, the compactness theorem. In addition, some familiarity with field theory, topology and probability will be beneficial.