# 22S-MATH-220C-LEC-1 Mathematical Logic

**Math 220C, Mathematical Logic and Set Theory, Spring 2022.**

##### Mondays 1-1:50pm and 2-2:50pm, Wednesdays 1-1:50pm, via zoom.

Itay Neeman

Office hours: Tuesdays 2-3pm, Thursdays 12-1pm, or by appointment.

** **

**Material:**

This is the third in a three part series of courses on Mathematical Logic and Set Theory. This part focuses on set theory. The main result we will cover is the consistency of the continuum hypothesis. We will begin with a quick review of the axioms of ZFC and a development of basic set theoretic notions and tools, for example ordinals and transfinite recursion, from the axioms. We will then define Gödel's constructible universe L and study some of its properties, including condensation, the continuum hypothesis, and combinatorial principles such as ⋄ and Suslin trees. We will finish with some material on large cardinals, and show that the existence of a measurable cardinal implies that V is not equal to L.

**Text:**

A good reference for the material we cover is the book *Set Theory, an introduction to independence proofs *by Kunen. We will cover most of the material in Chapters 1, 3, 4, and 6 of the 1983 edition. Another good reference is the book *Set Theory* by Thomas Jech. It covers a great deal more than we can cover in one term.

**Remote teaching:**

This course will be taught remotely through zoom. All lectures will be recorded, and students are encouraged to view the recordings following the lectures, as a way of strengthening your class notes.

**Grading**

The final grade will be based on homework (roughly 30%), a final exam (roughly 50%), and attendance (roughly 20%).

Attendance is required with the camera on. Missing 12 or more hours will result in zero attendance credit, missing 3 or fewer will result in full attendance credit, and anything between will be interpolated linearly. Exceptions to this can be given for valid reasons, please contact me if anything is preventing you from attending all lectures.

Exam questions will typically ask for proofs or parts of proofs that were covered in class or in homework assignments, or some variants of these.

**Homework assignments**

The assignments are listed here. They are due usually by Monday morning each week, ideally submitted online, and otherwise by paper during class. Some are taken from past qualifying exams in Logic, and these are listed as TYY.NN where YY is the exam year, T is the exam term, and N is the question number. Some are taken from Kunen's book, and these are listed as KC.N where C is the chapter number and N is the exercise number. You can view the first chapter of the book online.