Question: (On exercise 5.8 3) Is there any example of an irreducible set $F$ such that there's a power of $F$ which is NOT irreducible? For constructible sets, that's not possible.

More comments on section 4.

Sonat noticed that a good definition of locus(a/A) depends of one of two things:

• Either you have essential uncountability (EU) in $M$ (that implies $\omega_1$-compactness in $M$ and so DCC in any elementary extension) , or
  
• $A$ is a subset of $M$ (in which case the locus is actually a basic predicate).

Finally we decided, from now on, to assume that when it is mentioned an $A$ set, $A\subseteq M$. So far, this assumption has solved most of our problems with the proofs.

An issue that came up today while we were discussing what we're gonna talk about tomorrow is the distinction between predicates and actual sets. Zilber uses both notations indistinctively and sometimes it is hard to dilucidate which one is the object he is talking about.

May 19th session.

On May 19th. Sonat and I will be talking about section 4. We will go over some of the proof and, If time permits, we will even discuss with the attendands a few exercises.

First meeting and general info.

Hello, this is a weblog to complement the summer seminar on Zariski Geometries we will be running during summer 2005.

The notes we will follow are available at http://www.maths.ox.ac.uk/~zilber/s.pdf.

The first meeting will be on friday the 13th at 4:00 pm at Crane Alley. An informative e-mail will be sent to the Urbana logic group announcing it.

I guess we can use this space to post questions we might come up with during the sessions and have some extra discussion. If you're interested on being able to post entries here, you should create a blogger account and then contact me so I can add you to the list of contributors of the blog. Of course, everybody, even if you're not one of the aformentioned contributors, can write comments clicking on the comment link at the end of each entry and filling up the corresponding form.

May the force be with us.