# Instructor Class Description

Time Schedule:

**Bob Alan Dumas**

PHIL 472

Seattle Campus

### Axiomatic Set Theory

Development of axiomatic set theory up to and including the consistency of the Axiom of Choice and Continuum Hypothesis with the Zermelo-Fraenkel Axioms.

**Class description**

We will begin the course with a brief treatment of the axioms of Zermelo-Fraenkel set theory (ZF), ordinal numbers, and cardinality. We will define the axiom of choice (AC) and prove the numerous useful equivalences in ZF. We will also cover elementary cardinal arithmetic, the continuum hypothesis, and the generalized continuum hypothesis. We will define the axiom of constructibility (V=L), and show that if ZF is consistent then ZF + V=L is consistent. We then show that AC and CH hold in ZF + V=L, hence ZFC + CH is consistent, provided that ZF is consistent.
TEXT: Set Theory, Jech.

**Student learning goals**

**General method of instruction**

**Recommended preparation**

**Class assignments and grading**

*The information above is intended to be helpful in choosing courses. Because the instructor may further develop his/her plans for this course, its characteristics are subject to change without notice. In most cases, the official course syllabus will be distributed on the first day of class.*

Last Update by Annette R. Bernier

Date: 08/12/2009