An Exposition on Radin Forcing

Abstract

Chapter 1 Historical Introduction The origins of set theory date back to the late 19th century, due to the work of Georg Cantor. In Cantor’s theory, the relative size, or cardinality, of sets is based on whether they can be put into one-to-one correspondence with each other. He first showed how to put the natural numbers and algebraic numbers into such a correspondence, thereby establishing that these sets have the same cardinality. He then showed that no such bijection exists between the set of natural numbers and real numbers, meaning that the continuum represents a strictly larger infinite set.