Date: Mon, 6 Feb 2023 11:28:56 +0200 (EET) Message-ID: <76905580.40104.1675675736274@wiki-1.it.helsinki.fi> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_40103_1386695206.1675675736274" ------=_Part_40103_1386695206.1675675736274 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Elements of set theory, spring 2014

# Elements of set theory, spring 2014

Fan Yang

10 sp.

### Type

Intermediate studies

### Prerequisites  = ;

No special prerequisites.

### Description

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

### Lectures

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

Easter Holiday 17.-23.4.

week 3 (Jan 14, 16) chapter 1-2: introduction, a= xioms and operations ST_1_ht.pd= f Jan 16, 22:30
= week 4 (Jan 21, 23) = chapter 3: ordered pairs, relations and orderings,
equivalence relations= . chapter 7: partial orderings
= ST_2_ht.pdf = Jan 24, 20:50
= week 5 (Jan 28, 30) chapter 3: equivalence relations, = functions, axiom of choice = ST_3_ht.pdf = Jan 31, 13:40
= week 6 (Feb 4, 6) = chapter 4: construction of natural numbers,
transitive sets, ordering o= n =CF=89, recursion theorem
= ST_4_ht.pdf = Feb 6, 23:30
= week 7 (Feb 11, 13) = chapter 4: arithmetic. chapter 5: integers = ST_5_ht.pdf = Feb 13, 23:30
week 8 (Feb 18, 20) chapter 5: rational numbers, Dedek= ind cuts ST_6_ht.pdf Feb 20, 23:50
week 11 (Mar 11, 13) chapter 5: real numbers ST_7_ht.pdf Mar 13, 17:00
week 12 (Mar 18, 20) chapter 6: equinumerosity, finite = sets, cardinal arithmetic ST_8_ht.pdf Mar 20, 16:40
week 13 (Mar 25, 27) chapter 6: cardinal arithmetic, or= dering cardinal numbers ST_9_ht.pdf Mar 27, 17:00
= week 14 (Apr 1, 3) = chapter 6: ordering cardinal numbers, axiom of choice,
countable sets, = absorption law of cardinals
= ST_10_ht.pdf = Apr 3, 21:40
week 15 (Apr 8, 10) chapter 7: well orderings, isomorp= hisms, ordinal numbers ST_11_ht.pdf Apr 10, 17:00
week 16 (Apr 15)
week 17 (Apr 2= 4)
= chapter 7: ordinal numbers, transfinite induction and recursion,
debts p= aid
= ST_12_ht.pdf = Apr 24, 17:20
week 18 (Apr 29) chapter 7: debts paid, rank ST_13_ht.pdf Apr 29, 14:20

### Exams

There will be a midterm exam and a final exam.

Date Time Place
Midterm Exam Feb 28 10-12 B120
= Final Exam May 9 = 10-12 = B321

Bibliography

 Textbook: H. Enderton, Elements of Set Theory, Academic Press. (Errata) References: Introduction to Set Theory, Karel Hrbacek and Th= omas Jech, 3rd Edition, Marcel Dekker. Set Theory for the Working Mathematician,  = Krzysztof Ciesielski, Cambridge Unive= rsity Press.

### Exercise class

Group Day Time Place Teacher
1. Friday 10-12 B321 Miguel Moreno

### Exercises

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 =C3=97 6 poin= ts =3D) 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 awarde= d 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
=E2=89=A540% 1
=E2=89=A550% 2
=E2=89=A560% 3
=E2=89=A570% 4
=E2=89=A580% 5
=E2=89=A590% 6

### Registration

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