Abstract

Let \ be an infinite discrete set of measurable cardinals. It is shown that generalized Prikry forcing to add a countable sequence to each cardinal in \ is subcomplete. To do this it is shown that a simplified version of generalized Prikry forcing which adds a point below each cardinal in \, called generalized diagonal Prikry forcing, is subcomplete. Moreover, the generalized diagonal Prikry forcing associated to \ is subcomplete above \, where \ is any regular cardinal below the first limit point of \.