On a theorem of silver

A recent theorem of Silver, in its simplest form, states, that if ω < cf(k) < k and 2^λ=λ⁺ for all λ < k, then 2^k=k⁺. Silver's proof employs Boolean-valued as well as nonstandard models of set theory. In the present note we give an elementary proof of Silver's theorem in its general form.