If κ is an infinite cardinal, then X ⊆ [special characters omitted] is called κ-dense if between any a < b, both in [special characters omitted], there are exactly κ elements of X. In these terms, a famous result of Cantor says that in every model of set theory all [special characters omitted]-dense sets of reals are isomorphic (to [special characters omitted]). This result cannot be directly extended, however, since for κ = [special characters omitted] there exist models of set theory in which not all [special characters omitted]-dense sets are isomorphic. On the other hand, Baumgartner has shown by the method of iterated forcing that assuming the consistency of set theory, there does exist at least one model of set theory in which all [special characters omitted]-dense subsets are isomorphic. We present here a detailed, yet expository, account of Baumgartner's result and discuss its relevance to the Proper Forcing Axiom of contemporary set theory.