Math 141b Mathematical Logic II

Welcome to Math Math 141b Mathematical Logic II! In this course, we will explore the various incompleteness results that limit mathematics, most notably the incompleteness theorems of Kurt Gödel (pictured above).

Class meets in SC 310 on TR 9-10:15am.

The official course textbook will be Per Lindström, Aspects of Incompleteness. Note: The book link will take you to a place that you can download the textbook for free from the publisher (at least on a wired, Harvard connection). This will be supplemented with various notes.


  • The course policies are described throughout this webpage. They are also outlined in the syllabus.
  • The most important thing is that you respect your fellow classmates and yourselves in all interactions. We've all taken different paths to get here, but we've come together for the shared goal of learning fantastic incompleteness results.
  • Homework: 70%
  • Final: 30%

  • Email:
  • Office: Science Center 238

    My office is kind of hard to find the first time, so here's a map (follow the red path, it starts at the second floor elevators). If you come out of the main elevators on the second floor, take a u-turn to your left and go all the way to the end of the hallway. Go through the door at the end to enter a cluster of math department offices. If you keep walking back in that direction, you'll find my office.
  • Office hours:
    • Tuesday 1-2pm
    • Thursday 2-3pm
    Office hours are a great time to come and ask questions about course material and/or homework. Note that my office hours are not right before homework is due. This is by design, to encourage you to start looking at the homework early.

Assignment .pdf .tex Due Date
Week 1 PS1 PS1 Feb. 7
Note the nonstandard Thursday due date!
I added the necessary hypothesis "with no finite models" to problem 1
Week 2 PS2 PS2 Feb. 12
Week 3 PS3 PS3 Feb. 19
Week 5 PS5 PS5 Mar. 5
Week 6 PS6 PS6 Mar. 12
Week 7 PS7 PS7 Apr. 9

  • Actively engaging with the material is the best way to learn math. I want to give you as much opportunity to do so as possible, so we will have weekly problem sets due Wednesday. In particular, you can turn in problem sets either in class or via email to the CAs (please include all three on the email). Either way, the problem sets are due by the end of class.
  • Math is a team sport and the best way to learn is to find classmates and friends to work on problem sets with. I really encourage you to work with people in this class both on completing the problem sets and gaining a better understanding of the material in general.
  • Math Night is a great place to meet up with people in your class and in the larger department. Note that the homework is cleverly scheduled to be due the class after Math Night each week.
  • To really drive home that I'm serious about collaboration and to help you find people to work with, for the first three assignments, I will be assigning you groups to work with. I'll send out emails to groups around the same time that I post assignments. These aren't the only people you can work with, but I'd like you to try working in these groups for at least an hour. If you do, then your group will get 10 bonus points on the assignment. Make sure everyone writes at the top of their homework that y'all worked together so the grader's know.

    If you run into problems meeting up with your group (some group members don't want to meet, but others do; there's no time that works for everyone; etc.), let me know and I'll help resolve the problem.
  • We all make mistakes, and the best thing to do is to learn from these mistakes. Thus, if you get back a problem set that you wish you had done better on, you can resubmit up to one week after the problem sets are returned. You're eligible for up to half of the points missed. Also, to avoid gaming of this combined with no late homework, you can only resubmit problems that you actually submitted in the first place.
  • The homework is designed to help you check, solidify, and deepen your understanding of the material. Since this course builds on itself (as most do), this is less helpful if you delay it. Thus, late homework is not accepted.
  • Homework should be turned in by the end of class, either a hard copy or an email.
  • I understand that things come up, and so you are given two 'grace' assignments throughout the semester. These are assignments that you can turn in up to one week late. If something comes up outside of the scope of these two grace assignments, please discuss it with me individually.
  • I'm happy to accommodate any modifications suggested by the Accessible Education Office (AEO). Please be sure to provide me with the introductory letter as soon as possible.
  • I expect students at all time to follow Harvard's Honor Code and practice academic integrity. I understand that the line between collaboration and plagiarism can be murky on problem sets, but the following is a good (and oft quoted) rule of thumb: working together is fantastic, but you should always be able to separate and right up your solutions individually. If you have any questions, please don't hesitate to ask.
If you have any questions, please feel free to contact me at
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