Week 
Topic 
Presentations 
Remarks 
Week 1 Jan 7  11 
Definition of the real numbers
as Dedekind cuts 
read about the reals as Cauchy
sequences Goldrei: 2.13, 2.19 

Week 2 Jan 14  18 
Definition of the natural numbers Induction and the ordering on N First axioms of set theory 

Week 3 Jan 21  25 
Presentation: Theorem 3.2.2 N is linearly ordered Presentation: Theorem 3.2.4 N is wellordered Axioms for set theory: relations, functions, orderings 
Kris, Emily, Chelsea; Mohdeep 
Exercises: 3.1.1, 3.2.2,
3.2.3, 3.2.7, 3.2.8, 3.2.11, 3.2.13 Scribes: Adam, Josh L. 
Week 4 Jan 28  Feb 1  Presentation: Lemma 2.3.11 Presentation: Theorem 2.3.12 Presentation: Theorem Exercise 2.3.9 The recursion theorem: arithmetic 
SeJin Josh L. Adam 
Exercises: Chapter 2: 1.6,
2.3, 3.6, 3.7, Scribes: Nigel P., Sean 
Week 5 Feb 4  8 
Presentation: addition is
associative Presentation: multiplication is commutative Presentation: mult distributes over addn Cardinality, SchroderBernstein, pigeonhole principle 
Nigel S. Sean Nigel P. 
Exercises: think about how to
formulate and prove the statements for presentation, and also Ex 4.7
from chapter 3. Scribes: Chelsea and Mohdeep 
Week 6 Feb 11  15 
AxB=BxA A^2=AxA Ax(B\cupC)=AxB\cupAxC A^(B\cupC)=A^BxA^C C^AxB=(C^B)^A comparing cardinalities of infinite sets 
Mohdeep Emily Kris 
Exercises: read chs 4.1 and
4.2 From Chapter 4: 2.1, 2.2, 2.3, 2.4, 2.5 Scribes: SeJin and Nigel S. 
Reading Week Feb 18  22 

Week 7 Feb 25  Mar 1 
ch 4 Lemma 2.2 ch 4 Corollary 2.2 Cardinals, the continuum hypothesis 
Nigel P. Josh 
Homework problems given in
class Scribes: Kris, Emily 
Week 8 Mar 4  8 
Ch 4 Ex 4.4 Ch 4 Ex 4.6 Wellordered sets and ordinals 
Sean Mohdeep and Nigel S. 
Read Chapter 4, section 4 on
Linear Orderings Problems from Ch 4: 4.2, (4.4, 4.6), 4.10, 4.11, 4.12 scribes: Adam, Josh 
Week 9 Mar 11  15 
Thm 6.2.6 a, b, c Thm 6.2.6 d Lem 6.1.4 Cor 1.5 Axiom of replacement; transfinite induction 
Chelsea SeJin Kris Nigel S. 
Read chapter 6, sections 1
and 2 1.1, 1.2, 1.5 2.4, 2.7, 2.8 scribes: Nigel P. Sean, Mohdeep 
Week 10 Mar 18  22 
Thm 6.5.3 Thm 6.5.8 Initial ordinals and alephs 
Josh Nigel P. 
Read Theorem 6.4.5, and
sections 6.4, 6.5 Problems: 6.3.3, 6.3,4, 6.5.4, 6.5.5, 6.5.10 scribes: Chelsea, Emily, SeJin 
Week 11 Mar 25  29 
Thm 7.1.9 (b) Axiom of choice 
Adam 
Read chapter 7, section 1 and
2 Problems: 7.1.6, 7.1.5, 7.2.5, 7.2.6 scribes: Nigel S, Kris 
Week 12 Apr 1  5 
Axiom of choice  Final homework set 

Week 13 Apr 8  10 
Discussion of consistency 