Summary: SHORT EXTENDER FORCING
MOTI GITIK AND SPENCER UNGER
These notes are based on a lecture given by Moti Gitik at the Appalachian Set
Theory workshop on April 3, 2010. Spencer Unger was the official note-taker. Dur-
ing the lecture Gitik presented many forcings for adding -sequences to a singular
cardinal of cofinality . The goal of these notes is to provide the reader with an
introduction to the main ideas of a result due to Gitik.
Theorem 1. Let n | n < be an increasing sequence with each n +n+2
strong, and =def supn< n. There is a cardinal preserving forcing extension in
which no bounded subsets of are added and
In order to present this result, we approach it by proving some preliminary
theorems about different forcings which capture the main ideas in a simpler setting.
For the entirety of the notes we work with an increasing sequence of large cardinals
n | n < with =def supn< n. The large cardinal hypothesis that we use
varies with the forcing. A recurring theme is the idea of a cell. A cell is a simple
poset which is designed to be used together with other cells to form a large poset.