Topic summary

Strong limit cardinal

Strong limit cardinal

Extracted from the Wikipedia article Limit cardinal.

A cardinal λ is a strong limit cardinal if λ cannot be reached by repeated powerset operations. This means that λ is nonzero and, for all κ < λ, 2 < λ. Every strong limit cardinal is also a weak limit cardinal, because by Cantor's theoremκ ≤ 2 for every cardinal κ, where κ denotes the successor cardinal of κ.