## Set theory seminar -Forcing axioms and inner models -Intermezzo

September 30, 2008

This posting complements a series of talks given at the Set Theory Seminar at BSU from September 12 to October 24, 2008. Here is a list of links to the talks in this series:

• First talk, September 12, 2008.
• Second talk, September 19, 2008.
• Third talk, September 26, 2008.
• Fourth talk, October 3, 2008.
• Fifth talk, October 10, 2008.
• Sixth talk, October 17, 2008.
• Seventh talk, October 24, 2008.

[Version of October 31.]

I’ll use this post to provide some notes about consistency strength of the different natural hierarchies that forcing axioms and their bounded versions suggest. This entry will be updated with some frequency until I more or less feel I don’t have more to add. Feel free to email me additions, suggestions and corrections, or to post them in the comments. In fact, please do.

## 580- Topics in Set Theory. ANNOUNCEMENT

September 30, 2008

This Spring I will be teaching Topics in set theory. The unofficial name of the course is Combinatorial Set Theory.

We will cover diverse topics in combinatorial set theory, depending on time and the interests of the audience, including partition calculus (a generalization of Ramsey theory), cardinal arithmetic, and infinite trees. Time permitting, we can also cover large cardinals, determinacy and infinite games, or cardinal invariants (the study of sizes of sets of reals), among others. I’m open to suggestions for topics, so feel free to email me or to post in the comments.

Prerequisites: Permission by instructor (that is, me).

Recommended background: Knowledge of cardinals and ordinals. A basic course on set theory (like 502: Logic and Set Theory) would be ideal but is not required.

The course may be cancelled if not enough students enroll, which would make us all rather unhappy, so don’t let this happen.

## 175, 275 -Homework 5

September 30, 2008

Homework 5 is due Tuesday, October 7, at the beginning of lecture. Same remarks as before apply.

175: Section 7.1, exercises 20, 30, 32, 42.
Section 7.2, 40.
Section 9.3, exercise 23.
Each problem is worth 2 points; there are 2 extra credit points.

275: Section 12.1, exercises 13-18, 44.
Section 12.2, exercises 36, 54.
Section 12.3, exercises 21, 22, 30.
The exercises in section 12.3 are worth 1 point each, the combined exercise 12.1.13-18 is worth 3 points, the other exercises are worth 2 points each; there are two extra credit points.

## 175, 275 – Midterm 1

September 30, 2008

The first exam was Friday, September 26, during lecture. This exam is worth 10% of the total grade. Books, notes, and calculators were allowed.

Failure to take the exam was graded as a score of 0.

175: The exam covered Chapters 6 and 9 of the textbook (and assumed knowledge of Calc I). Exam, Graph.

275: The exam covered Chapters 10 and 11 of the textbook (and assumed knowledge of Calc I and II). Exam, Graph. (Typo: In problem 2.d, the equation of the plane must be $x+y-2z=2$.)