Teaching - Jonathan Kirby

Current Teaching

Spring 2007 - Calculus III

MWF at 11am, Taft Hall, room 317
Office hours: Monday 2-3pm, Tuesday 10-11am, Wednesday 2-3pm
My email address is kirby at math.uic.edu.
See the course webpage for more details.

Homework will be due in on Wednesday each week. Please staple your work together. Unstapled work will not be graded.

Some general notes

Past Teaching

Fall 2006 - Model Theory 1

MWF at 9am, Taft Hall, room 215

I plan to give out one homework about every two weeks. The course assessment will be based on these homeworks.
Homework 2 (pdf)
Homework 3 (pdf)
Homework 4 (pdf)
Homework 5 (pdf)

The course will be based on David Marker's book, Model Theory: An Introduction. We will cover most of chapter 2, some of chapter 3, and most of chapter 4. We may also cover some topics from later chapters.

Course topics:

The compactness theorem, and proof via a Henkin construction. Elementary classes. Complete theories and Vaught's test. The Lefschetz Principle and Ax's theorem on injective polynomial maps. Elementary embeddings, the method of diagrams and the Upward Löwenheim-Skolem theorem. The Tarski-Vaught test and the Downward Löwenheim-Skolem theorem. The elementary chain lemma. Universal theories and substructures.

Back-and-forth arguments: Cantor's theorem on dense linear orders. Sets definable with and without parameters. Quantifier elimination for DLO and ACF.

Partial and complete n-types over a set of parameters. Realizing types lemma. Automorphisms and types in elementary extensions. Partial elementary maps (extension of back-and-forth method). The Stone spaces of types. Isolated types, principal types and their equivalence. The subset of n-types realized in a model is dense.

The omitting types theorem. Lindenbaum algebras and the Ryll-Nardzewski theorem. Atomic and prime models. Uniqueness of prime models. The equivalence of prime with countable and atomic (for countable languages). Saturated and universal models. Uniqueness of saturated models. Homogeneous models. Saturated = universal and homogeneous.

Criterion for the existence of prime models. Criterion for the existence of countable saturated models. Prime model extensions. Applications of saturated models. The number of countable models of a theory.

Some algebraic examples.