INSTRUCTIONS FOR LESS EXPERIENCED PARTICIPANTS 

1. Please try to get some sense of the material on fine structure theory from the paper

Schindler-Zeman: Fine structure theory, Handbook of Set Theory, Springer 2010.

Try to understand the idea of uniform Sigma_1 Skolem function and that of a projectum.

To get the general sense keep the technicalilites at the minimum by following these rules:
(a) Always work only with the first projectum.
(b) Try to work in L whenever possible.
(c) When focusing on the first projectum and L, you may replace the notion "r-Sigma_1" with just "Sigma_1". This should allow you  to focus on the  notions  of  Skolem function and projectum without toom much distraction.

For other basic information you can consult also Jensen's original paper

Jensen: Fine structure of the constructible hierarchy, Annals of Mathematical Logic 2

Concerning Jensen's paper, do NOT read past the section on the first projectum, as the text then diverges substantially from the modern treatment of the subject.

2. Read Section 19 "Iterated Ultrapowers" from the book

Kanamori: The higher infinite.

3. Read through basic  facts on extenders from 

Martin-Steel: Proof of Projective Determinancy, Journal of American Mathematical Society 2(1), 1989, 71-125

Also, the Schindler-Zeman paper above has some information on extenders.

4. Work through the construction of a "pseudoultrapower" from

Zeman: Inner models and large cardinals, DeGruyter 2002

This is Section 3.6. This is an important technique that will be used in sevaral arugments discussed during the program. We will go over this in the school, but it would be good if you have some prior contact with the construction. Other literature uses the term "ultrapower by long extender" instead of "pseudoultrapower". The construction is actually an ultrapower construction, but instead of an ultrafilter/extender it uses a  map. The Schindler-Zeman paper also has some information in the topic. Here is a recommendation how to read the construction from Section 3.6: The variant written in Section 3.6 is a fine structural variant. To start with, do just the coarse, that is, non-fine structural variant. For this, put k=0 and ignore n in the definition of $\Gamma^k(\sigma,M)$.  Then
$\Gamma^0(\sigma,M)$ is the set of all functions $f:\gamma\to M$ such that $\gamma<\tau$ and $f\in M$.
So you can pretend that you are constructing something like an ultrapower.

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Last modified: May 12, 2012