Elements of set theory, spring 2014


Fan Yang


10 sp.


Intermediate studies


No special prerequisites.


Set theory is widely accepted as the foundation of mathematics. In this course, we will go through chapter 1-7 of Enderton's book Elements of Set Theory. The following topics will be covered: axioms and operations on sets, relations and functions, natural numbers, construction of real numbers, cardinal numbers, axiom of choice, orderings and ordinal numbers.


Weeks 3-8 and 11-18, Tuesday 12-14 in room B322 and Thursday 14-16 in room DK117.

Easter Holiday 17.-23.4.

contentshandoutlast modified
week 3 (Jan 14, 16)chapter 1-2: introduction, axioms and operations
Jan 16, 22:30
week 4 (Jan 21, 23)chapter 3: ordered pairs, relations and orderings,
equivalence relations. chapter 7: partial orderings

Jan 24, 20:50
week 5 (Jan 28, 30)chapter 3: equivalence relations, functions, axiom of choice
Jan 31, 13:40
week 6 (Feb 4, 6)chapter 4: construction of natural numbers,
transitive sets, ordering on ω, recursion theorem 

Feb 6, 23:30
week 7 (Feb 11, 13)chapter 4: arithmetic. chapter 5: integers
Feb 13, 23:30
week 8 (Feb 18, 20)chapter 5: rational numbers, Dedekind cuts
Feb 20, 23:50
week 11 (Mar 11, 13)chapter 5: real numbers
Mar 13, 17:00
week 12 (Mar 18, 20)chapter 6: equinumerosity, finite sets, cardinal arithmetic
Mar 20, 16:40
week 13 (Mar 25, 27)chapter 6: cardinal arithmetic, ordering cardinal numbers
Mar 27, 17:00
week 14 (Apr 1, 3)chapter 6: ordering cardinal numbers, axiom of choice,
countable sets, absorption law of cardinals

Apr 3, 21:40
week 15 (Apr 8, 10)chapter 7: well orderings, isomorphisms, ordinal numbers
Apr 10, 17:00
week 16 (Apr 15)
week 17 (Apr 24)
chapter 7: ordinal numbers, transfinite induction and recursion,
debts paid

Apr 24, 17:20
week 18 (Apr 29)chapter 7: debts paid, rank
Apr 29, 14:20


There will be a midterm exam and a final exam.

Midterm ExamFeb 2810-12B120
Final ExamMay 910-12B321


Textbook:H. Enderton, Elements of Set Theory, Academic Press. (Errata)
References:Introduction to Set Theory, Karel Hrbacek and Thomas Jech, 3rd Edition, Marcel Dekker.

Set Theory for the Working Mathematician,  Krzysztof Ciesielski, Cambridge University Press.

Exercise class

1.Friday10-12B321Miguel Moreno


Date of exercise class
1.Jan 24
2.Jan 31
3.Feb 7
4.Feb 14
5.Feb 21
6.Mar 14
7.Mar 21
8.Mar 28
9.Apr 4
10.Apr 11
11.Apr 25
12.May 2
13.No exercise class


To pass the course, you need to take two course exams (midterm and final). Attending only one exam (even if you score full marks) is not sufficient. From each of the two exams, you can score (4 questions × 6 points =) 24 points. The passing mark for the course is around 24 points (the exact passing mark will be decided by the lecturer at the end of the semester according to the overall performances of the students). 

By solving a certain amount of the exercise problems, you will be awarded extra points (see the table below for details). "Solving" here means that you have honestly tried to give solutions to the problems.

percentage of exercise
problems solved
extra points


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