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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.

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics