[jakef]

This article is talking about the cardinality of two very specific sets. Before, many believed that t > p, but many believed that this was not provable in ZFC. Both sets contain only sets of integers, so their cardinality is bounded above by the cardinality of the real numbers (the continuum). Some people believed that this result was related to the Continuum hypothesis, and so was only provable one way or the other if you assume the CH or its negative.

As it turns out, both sets have the same cardinality (that of the real numbers) AND it is provable in ZFC.

The title is a little misleading, its really saying that two infinite sets are the same size, but prior to this their cardinality was unknown, and it wasn't even known if the cardinality was provable in ZFC.