List of participants in this workshop

Lecture notes by Moti Gitik and Spencer Unger (PDF)

The basic setting for such forcings is as follows.
We have a singular cardinal κ
of countable cofinality and an increasing sequence
κ_{n} for n < ω
whose supremum is κ.
Each κ_{n} is a large cardinal in that it carries an extender
E_{n}
with critical point κ_{n}.
But κ_{n} is not "too large" in that the strength of
E_{n} is
"much less" than κ _{n+1}.
In particular, we are not assuming that κ is overlapped
by any extender.
Using such a sequence of extenders, we define a forcing
that blows up the power of κ, that is, makes
2^{κ} > κ^{+}.

Such forcings allow us to reduce known consistency strength upper bounds of certain instances of the Singular Cardinals Hypothesis to the optimal ones. In addition, they allow us to construct models with PCF configurations that other methods fail to produce. We hope that further development of these forcing notions may lead to progress on basic problems of cardinal arithmetic like the Shelah Weak Hypothesis and the PCF Conjecture.

We plan to start the workshop with a forcing notion that uses an
overlapping sequence of extenders
E_{n} for n < ω to blow up the power of κ.
Then we modify the construction to one in which each E_{n}
has length (&kappa_{n})^{+n+2}
and calculate that 2^{κ}
= &kappa^{++} in the corresponding forcing extension.
Next we make 2^{κ} = &kappa^{+++}
but for this we prepare the ground model with a certain
preliminary forcing.
We discuss how these ideas can be used to make the gap
between κ and its power even larger.
Finally we turn to a certain cardinal arithmetic configuration called
*dropping cofinality*.

- James Cummings, "Iterated forcing and elementary embeddings", chapter in Handbook of Set Theory (PDF)
- Moti Gitik, "Prikry-type forcings", chapter in Handbook of Set Theory (PDF)

__Note__: There is a shortcut from the Shadyside Inn to CMU
that is very pleasant walk. Ask for directions at the registration desk.

The Shadyide Inn is less than 3/4 mile from CMU; you could walk, take a bus, or call the Shadyside Inn to pick you up.

(If you arrive early, you may want to meet others in the Mathematical Sciences Department lounge, 6220 Wean Hall.)

Taxis from the airport cost about $50.

Another door-to-door option is Super Shuttle at $27 per person in a shared van.

- Your name, university affiliation, mailing address, phone number and email address
- Your professional status and
- undergraduate students: please describe your background in set theory
- graduate students: please tell us your year and the name of your thesis advisor if you have one
- faculty: please tell us whether you hold a federal research grant

- A brief statement about your interest in the workshop
- An itemized estimate of your expected transportation expenses