課程資訊
課程名稱
基本集合論
Elementary Set Theory 
開課學期
107-1 
授課對象
文學院  哲學研究所  
授課教師
楊金穆 
課號
Phl7713 
課程識別碼
124EM2990 
班次
 
學分
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期五7,8,9(14:20~17:20) 
上課地點
哲研討室二 
備註
本課程以英語授課。C領域。
總人數上限:15人 
 
課程簡介影片
 
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課程概述

The course is designed for philosophy undergraduates specially interested in formal logic, philosophy of mathematics and philosophy of language and logic. The aim of this course is to provide a nodding acquaintance with elementary properties of sets and basic axioms of set theory. The study will be confined to the well-established Zermelo -Fraenkel set theory. (A course on Elementary Logic is usually assumed, though not so necessary)

Content
Preliminary

.1 Some naive assumptions of set theory
.2 Two aspects of set theory and the development of set theory: A historical survey
.3 The mathematical and philosophical significance of set theory
.4 A first-order language suitable for set theory

1 Basic Axioms for Sets

2 Functions

3 Relations

4. Natural Numbers

4.1 The axiom of infinity and the construction of - the set of natural numbers
4.2 Peano's postulates
4.3 Recursion theorems on and arithmetic of
4.4 Orderings on
4.5 Peano Systems and Extensions of natural numbers

5 Equinumerous sets and Schroder-Bernstein Theorem

6 Cardinal Numbers

6.1 The need for cardinality
6.2 Finite and infinite sets
6.3 The axiom schema of replacement
7 The Axiom of Choice and Countable Sets

7.1 The axiom of choice
7.2 Countable sets

8 The Arithmetic of Cardinal Numbers

8.1 Cardinal addition
8.2 Cardinal multiplication (product)
8.3 Cardinal exponentiation

9 Zorn's Lemma, Continuum Hypothesis and Some Variants of the Axiom of Choice

9.1 Zorn's Lemma
9.2 Continuum Hypothesis
9.3 Some equivalent variants of Zorn's Lemma

10 Well-orderings

10.1 Well-orderings of sets
10.2 The comparison theorem for well-ordered sets
10.3 Well -ordering Principle

11. Ordinals

11.1 The Notion of Ordinal Numbers
11.2 Some elementary properties of the ordinals
11.3 Ordinal numbers and cardinal numbers

12 Arithmetic of Ordinals

Appendix. Models of ZF- Set Theory

@. 1 Natural models of ZF - set theory
@.2 The class of infinite c 

課程目標
The aim of this course is to provide a nodding acquaintance with elementary properties of sets and basic axioms of set theory. 
課程要求
待補 
預期每週課後學習時數
 
Office Hours
 
參考書目
H.B. Enderton, Elements of Set Theory, New York: Academic Press, 1977.
K. Kunen, Set Theory - An Introduction to Independence Proofs, Amsterdam: North-Holland, 1980.
 
指定閱讀
H.B. Enderton, Elements of Set Theory, New York: Academic Press, 1977.
K. Kunen, Set Theory - An Introduction to Independence Proofs, Amsterdam: North-Holland, 1980. 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Class performance 
20% 
 
2. 
Weekly assignment  
30% 
 
3. 
End-of-term exam 
50% 
 
 
課程進度
週次
日期
單元主題
第1週
9/14  Preliminary 
第2週
9/21  Basic Axioms for Sets 
第3週
9/28  Functions 
第4週
10/05  Relations 
第5週
10/12  Natural Numbers 
第6週
10/19  Equinumerous sets and Schröder-Bernstein Theorem 
第7週
10/26  Cardinal Numbers 
第8週
11/02  Cardinal Numbers 
第9週
11/09  The Axiom of Choice and Countable Sets

 
第10週
11/16  The Arithmetic of Cardinal Numbers

 
第11週
11/23  The Arithmetic of Cardinal Numbers

 
第12週
11/30  Zorn's Lemma, Continuum Hypothesis and Some Variants of the Axiom of Choice

 
第13週
12/07  Zorn's Lemma, Continuum Hypothesis and Some Variants of the Axiom of Choice
Well-orderings
 
第14週
12/14  Ordinals 
第15週
12/21  Ordinals 
第16週
12/28  Arithmetic of Ordinals

 
第17週
1/04  Arithmetic of Ordinals

 
第18週
1/11  Final exam