Stanford Univ
Mathematics 161: Set Theory
(Philosophy 161--Enroll in Math 161)
Winter 2005-2006
Syllabus

#### Instructor: Ruy de Queiroz (Visiting Professor)

Office hours: Mo We 09:30-10:45am and by arrangement, Room 8, Bolivar House
Class hours: Tu Th 09:30-10:45am, Seminar Room, Bolivar House

#### Course description:

Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations. Natural numbers. The Recursion Theorem. Finite, countable and uncountable sets. Ordinal numbers. Alephs and cardinal arithmetic. The Zermelo-Fraenkel axiom system.

#### Prerequisites:

Phil 151, 152 (formerly 160A, B), or equivalents, or consent of the instructor.

#### Text:

Introduction to Set Theory, by Karel Hrbacek and Thomas Jech, (Third Edition, Revised and Expanded), Marcel Dekker, New York, 1999.

#### Other resources:

1. http://plato.stanford.edu/entries/set-theory
2. http://en.wikipedia.org/wiki/Set_theory
3. The joy of sets, Keith Devlin, Springer, 2nd edition, 1993.
4. Naive set theory, Paul Halmos, Springer, 1974.
5. Introduction to modern set theory, Judith Roitman, John Wiley, 1990.
6. Set theory, Robert Vaught, Birkhäuser, 1995.

### Calendar

Jan 10
Motivation: Cantor and the notion of infinity
GEORG CANTOR: THE BATTLE FOR TRANSFINITE SET THEORY (by Joseph W. Dauben)

Jan 12
Basic principles (axioms)
Elementary operations
(Handout1, Ch 1)
(Homework1 to be handed in by Wed 18)

Jan 17
Ordered pairs
Relations
(Handout2, Ch 2, Sect 1 and 2)

Jan 19
Functions
(Handout3, Ch 2, Sect 3)
(Homework2 to be handed in by Wed 25)

Jan 24
Equivalences and partitions
Orderings
(Handout4, Ch 2, Sect 4 and 5)

Jan 26
Orderings (cont.) (Hasse diagram)
(Homework3 to be handed in by Feb 1)

Jan 31
The natural numbers
Properties of natural numbers
(Handout5, Ch 3, Sect 1 and 2)

Feb 2
The recursion theorem
(Handout6, Ch 3, Sect 3)
(Homework4 to be handed in by Feb 8)

Feb 7
The recursion theorem (cont.)
Arithmetic of natural numbers
(Handout7, Ch 3, Sect 4)

Feb 9
Midterm

Feb 14
Cardinality of sets
Finite sets
(Handout8, Ch 4, Sect 1 and 2)

Feb 16
Countable sets
(Handout9, Ch 4, Sect 3)
(Homework5 to be handed in by Feb 22)

Feb 21
Linear orderings
(Handout10, Ch 4, Sect 4)

Feb 23
Complete linear orderings
Uncountable sets
(Handout11, Ch 4, Sect 5 and 6)
(Homework6 to be handed in by Mar 6)

Feb 28
Complete linear orderings (cont.)
Uncountable sets (cont.)

Mar 2
Cardinal arithmetic
The cardinality of the continuum
(Handout12, Ch 5, Sect 1 and 2)
(Homework7 to be handed in by Mar 10)

Mar 7
Well-ordered sets
Ordinal numbers
(Handout13, Ch 6, Sect 1 and 2)

Mar 9
The axiom of replacement
(Handout14, Ch 6, Sect 3) The Zermelo-Fraenkel axiom system

Mar 14
(No class)

Mar 16
(No class)

Mar 20 (confirmed!)
Final exam

Last updated: March 9, 2006, 09:25am PST