As a result of 50 years of development of the forcing technique, and its applications to many open problems in mathematics, there are now literally thousands of questions, in practically all areas of mathematics, that have been shown independent of ZFC. These include almost all questions about the structure of uncountable sets. One might say that the undecidability phenomenon is pervasive, to the point that the investigation of the uncountable has been rendered nearly impossible in ZFC alone (see however Shelah (1994) for remarkable exceptions).