The internal consistency of Easton’s theorem

An Easton function is a monotone function C from infinite regular cardinals to cardinals such that C(α) has cofinality greater than α for each infinite regular cardinal α. Easton showed that assuming GCH, if C is a definable Easton function then in some cofinality-preserving extension, C(α)=2α for all infinite regular cardinals α. Using “generic modification”, we show that over the ground model L, models witnessing Easton’s theorem can be obtained as inner models of L[0#], for Easton functions which are L-definable with parameters at most . And using a gap 1 morass, we obtain an inner model of L[0#] with the same cofinalities as L in which is a strong limit cardinal and equals .