FOR LESS EXPERIENCED PARTICIPANTS
1. Please try to get some sense
of the material on fine structure theory from the paper
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
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
3. Read through basic
facts on extenders from
Martin-Steel: Proof of
Projective Determinancy, Journal of American Mathematical Society 2(1),
Also, the Schindler-Zeman paper above has some information on
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
Last modified: May 12,