Easton's theorem

In set theory, Easton's theorem is a result on the possible cardinal numbers of powersets. Easton (1970) (extending a result of Robert M. Solovay) showed via forcing that the only constraints on permissible values for 2^κ when κ is a regular cardinal are

${\displaystyle \kappa <\operatorname {cf} (2^{\kappa })}$

(where cf(α) is the cofinality of α) and

${\displaystyle {\text{if }}\kappa <\lambda {\text{ then }}2^{\kappa }\leq 2^{\lambda }.}$