MATH 4LT3/6LT3
Topics in Logic: Set Theory
Fall 2023

Announcements:

Course Information:


Assignments, Tests, and Solutions:

Test Date (tentative):

There will be one 50-minute test held during the semester. The test will be held in-person during the scheduled lecture time on October 17.  The test will be worth 20% of your final grade.


Final Exam Information:

A final exam for this course will be scheduled by the registrar.  Details will be posted on the course website as they become available.



Lecture Schedule:

Lecture # Date topics covered reading/resources/comments
1 05/09/23 Course introduction, equinumerosity Chapter 2 from textbook
2 07/09/23 equinumerosity, continued Chapter 2
3 09/09/23 countability of the rationals, uncountability of the reals Chapter 2
4 12/09/23 Algebraic numbers, Schroder-Bernstein Theorem Chapter 2
5 14/09/23 Russell's paradox, first six axioms of ZFC Chapter 3
6 15/09/23 continued Chapter 3
7 19/09/23 ordered pairs, cartesian product Chapter 4
8 21/09/23 relations, cardinals, cardinal arithmetic. Chapter 4
9 23/09/23 Peano Systems.  Properties, existence Chapter 5
10 26/09/23 The Recursion Theorem, uniqueness of Peano Systems Chapter 5
11 28/09/23 Arithmetic operations, the well ordering of the natural numbers Chapter 5
12 29/09/23 continued, Assignment #1 due
 Chapter 5
13 03/10/23 well orderings Chapter 7
14 05/10/23 well orderings Chapter 7
15 06/10/23 transfinite recursion, Assignment #2 due (deadline extended to 10/10/23) Chapter 7
16 17/10/23 midterm test
17 19/10/23 transfinite recursion Chapter 7
18 20/10/23 Comparability of well orderings Chapter 7
19 24/10/23 Hartog's theorem Chapter 7
20 26/10/23 Hartog's theorem, The axiom of choice Chapter 8
21 27/10/23 The axiom of choice, Assignment #3 due Chapter 8
22 31/10/23 The axiom of choice Chapter 8
23 02/11/23 The axiom of choice Chapter 8
24 03/11/23 Choice's consequences Chapter 9
25 07/11/23 Cardinal arithmetic Chapter 9
26 09/11/23 best well orders, CxC = C in cardinality, cardinal arithmetic Chapter 9
27 10/11/23 Konig's Theorem, assignment #4 due Chapter 9
28 14/11/23 No class today
29 16/11/23 Axiom of Replacement Chapter 11
30 17/11/23 Axiom of Foundation, Writing Project topic due today Chapter 11
31 21/11/23 ordinals
 Chapter 12
32 23/11/23 ordinals
 Chapter 12
33 24/11/23 cardinals
 Chapter 12
34 28/11/23 cardinals, cumulative hierarchy
 Chapter 12
35 30/11/23 cumulative hierarchy
 Chapter 12
36 01/12/23 no class today
37 05/12/23 Kieran's lecture, course wrap up, writing project due


Matt Valeriote