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.