### Final Exam

The final exam is on

We will be holding extra office hours ahead of the exam. The time and location will be posted here, but you may also email for appointments.

### Last part of the course

We are now starting on the third part of the course: axiomatic set theory and the ZFC axioms.
This material is not covered in Enderton's book. However, there is a (freely available for UCSD students) book that we will be closely following:
Yiannis Moschovakis' "Notes on Set Theory". The permanent link for the library record for the electronic version of this book is
here. Make sure you are connected to the UCSD network and click the link
for "SpringerLink. Restricted to UC campuses". From that page, you will be able to download .pdf files of each chapter by clicking the chapter name
in the menu on the left and then choosing "Download PDF" on the top right corner of the displayed first page of the chapter.

You may find other textbooks to be good resources for axiomatic set theory. A few good choices are the first chapter of Ken Kunen's "Set Theory", Enderton's "Introduction to Set Theory, Devlin's "Joy of Sets", etc.

### Second exam

The second exam is on

A collection of practice problems and review material is now available on this page.

### First exam

The first exam is on

A collection of practice problems and review material is also available on this page.

### Welcome!

Welcome to MATH 160. This webpage will be your main source of information for this course. It will be updated frequently with announcements and assignments, so check back often. For example, after homework is due, you can find solutions to it posted on this website, and any worksheets discussed during sections will be available below, along with their solutions.

Important information about the textbook, homework, and exams is on the Schedule and Syllabus page. Also there, you can find a calendar with the current information on important dates for this course.

Below you can find all homework assignments and any additional handouts.

Exercises listed in parentheses ( ) are recommended but

- Homework Exercises 1
(Due 1/18) Solutions*Section 1.1:*(1), (2), 5;*Section 1.2:*(2), 3, (4), 5, 8a, (9), (12), 15;

- Homework Exercises 2
(Due 1/25) Solutions*Section 1.3:*1 only for group 3, 2, (4), (6);*Section 1.4:*(2)

*Section 1.5:*1a, 3, (5), (6), 9a, (9b), (10) - Homework Exercises 3
(Due 2/8) Solutions*Section 1.7:*12a,b, (12c);

*Section 1.7*:*A: Prove that soundness is equivalent to the statement "every satisfiable set of formulas is consistent."

B: Prove that completeness is equivalent to the statement "every consistent set of formulas is satisfiable".

*Section 2.1:*2, 3 - Homework Exercises 4
(Due 2/22) Solutions*Section 2.2 to hand in:*3, 5, 8, 9, 18 a;

*Section 2.2 recommended:*(1), (2), (4), (11), (12), (14), (15), (16), (18 b), (21), (26), (28) - Homework Exercises 5
(Due 3/14) Solutions*Section 2.5:*4, 6

*Connecting chapter 2 and ZFC:*The Axiom of Extensionality (AxI) can be written as

.

Prove that the converse is always true. Namely, prove that for any structure for the language of set theory, the sentence

is satisfied in the structure.

*Chapter 3 of Moschovakis on page 30: x3.1, x3.2 parts 1-3*

### Handouts

- No-stress-quiz 1
(Handed out 1/18) - No-stress-quiz 2
(Handed out 1/23) - No-stress-quiz 3
(Handed out 1/30) - No-stress-quiz 4 (with solutions!)
(Handed out 2/6) - No-stress-quiz 5
(Handed out 2/13) - No-stress-quiz 6
(Handed out 2/22) - No-stress-quiz 7
(Handed out 2/27) - Soundness and completeness of sentential logic.
(Posted 1/27) - Topology and compactness of sentential logic.
(Posted 2/3) - Practice problems for Exam 1.
(Posted 1/27) - Practice problems for Exam 2 -- now with numbered exercises!
(Re-posted 2/27) - Practice problems for Final Exam
(Posted 3/13) Solutions for Exercise 23 are available here(Posted 3/21)