# Set Theory Seminar, Spring/Summer 2012

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Coordinator: Zhou Yang (周杨)

Email: wooonderfulworld AT gmail DOT com

Mobile: 150 6815 1550 (514379)

Textbook: Zermelo-Fraenkel Set Theory, by S. Hayden and J.F. Kennison

## Schedule: 2013.03.16. - 2013.06.08. Saturday Morning, 09:00 - 12:00, 紫金港 东6-416

03.16. Chapter 1: Groundrules, speaker: 黄兆镇 周 杨

03.23. Chapter 2: Relations and Functions , speaker: 杨心宇

03.30. Chapter 3: Binary Operations, speaker: 王军啸

04.06. Chapter 4: Ordinals, Cardinals, and the Axioms of Choice, Sections 4.1 and 4.2, speaker: 林中一攀

04.13. Chapter 4: Ordinals, Cardinals, and the Axioms of Choice, Sections 4.3 and 4.4, speaker: 林中一攀

04.20. Chapter 5 The Axiom of Infinity and the Natural Numbers, Sections 5.1—5.2a, speaker: 武鹏

04.27. Break: Midterm

05.11. Chapter 5 The Axiom of Infinity and the Natural Numbers, Sections 5.3 and 5.4,
Chapter 6 The Integers and the Rational Numbers, speaker: 李云峰

05.18. Chapter 7 The Real and Complex Numbers, speaker: 翟宸宇

05.25. Chapter 8 Transfinite Arithmetic, Sections 8.1—8.4 speaker: 林中一攀

06.01. Chapter 8 Transfinite Arithmetic, Sections 8.5—8.7 speaker:

06.08. Appendix Other Axioms and Approaches for Set Theory, speaker: 周 杨

If you want to participate in the seminar, please contact the coordinator.

pdf file

## Introduction

For those who want to major in mathematics, set theory is a good place to start.
This gives you more insight into what mathematics is all about.
It gives you a good training in logical and abstract thinking.
It also provides you the precise definitions of some of the most often used concepts in mathematics,
such as function, equivalence relation, binary operation, and ordinal and cardinal numbers.

Set theory is a relatively new field in modern mathematics. It serves as a foundation of
mathematics. In this seminar, we will study the ZFC axioms of set theory, and learn how
to formalize objects in mathematics(such as the natural and real numbers) in this axiomatic
system. Some fundamentals of algebra and topology will also be covered.
(These parts may be eliminated since in past set theory seminars, we usually did not have enough
time for the last chapter on transfinite induction)

This is an introductory seminar to set theory. Advanced topics in set theory,
such as Goedel's Completeness and Incompleteness Theorem, the independence proofs and large cardinals, will not be mentioned,
because they are irrelevant to everything you will learn in undergraduate level.
Unfortunately, no one in China is studying set theory, although it is very interesting and
worth studying.

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