 This raises the question of whether one can “control” the size of 2ℵδ with a weaker assumption than that ℵδ is a singular cardinal of uncountable cofinality such that GCH holds below ℵδ. The natural hypothesis to consider is that ℵδ is a singular cardinal of uncountable cofinality which is a strong limit cardinal, that is, that for all α &lt; ℵδ, 2α &lt; ℵδ. In 1975 Galvin and Hajnal proved (among other things) that under this weaker assumption there is indeed a bound: 