Higher-dimensional forcing
Abstract
Description
This is an overview about a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along $ω_1$ is given. Then its direct limit satisfies ccc by a well-known theorem on finite support iterations. However, this limit has size at most $ω_1$. To get larger forcings, we do not consider linear systems but higher-dimensional systems which are indexed along simplified morasses.