User blog:Leftunknown/Inaccessible Cardinal

Defined as a cardinal which cannot be obtained using arithmetic operations on cardinals.

A cardinal is also inaccessible, if it is uncountable, it is not a sum of K cardinals which are smaller than K, and a < K = 2a < K. Thus, no amount of power-setting of infinities is capable of constructing a cardinal which is inaccessible.