SHORT EXTENDER FORCING MOTI GITIK AND SPENCER UNGER Summary: SHORT EXTENDER FORCING MOTI GITIK AND SPENCER UNGER 1. Introduction 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 n - 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. Collections: Mathematics