## Breach

May 16, 2008

This was a fun movie to watch. Based on a true story, the way that Hollywood productions are based on things, but it actually stays closer to the facts than I expected. Chris Cooper plays FBI agent Robert Hanssen, perhaps the most notorious mole within the American intelligence community. Hanssen was arrested in 2001, and was convicted to life without parole for spying for the Russians for more than 20 years.

The movie tells the story of Eric O’Neill, the FBI agent who was ultimately responsible for obtaining the evidence that led to the arrest of Hanssen. It shows several of the methods that Hanssen used to pass information, the tactics that the Special Surveillance Group used while following Hanssen, Hanssen’s almost fanatic religious beliefs, and even some of his peculiar private customs.

I enjoyed this movie quite a bit. On the other hand, The Good Sheppard, released at about the same time, a fictional history of the CIA that I was looking forward to and received a much larger amount of publicity,  proved a peculiar disappointment.

## 116c- Lecture 14

May 16, 2008

We defined absoluteness of formulas with respect to two classes $M\subset N$; for example, every $\Delta_0$ formula is absolute with respect to $M$ and $V$, if $M$ is transitive. Once we establish a sufficiently long list of properties that are absolute with respect to a transitive model of (enough of) $\mathsf{ZFC}$ and $V$, we will be able to prove a few relative consistency results. The main application will be in the proof that Gödel’s constructible universe $L$ is a model of $\mathsf{ZF}$ (and of choice and $\mathsf{GCH}$), but a few other examples will be presented as well.

We proved the reflection theorem and some of its consequences, in particular, that no consistent extension of $\mathsf{ZF}$ is finitely axiomatizable.

An important application of these techniques is the use of basic model-theoretic tools to establish combinatorial facts. Some examples will be explored in the next homework set.