Easton's Theorem for Ramsey and Strongly Ramsey cardinals

Abstract

We show that, assuming GCH, if $\kappa$ is a Ramsey or a strongly Ramsey cardinal and $F$ is a class function on the regular cardinals having a closure point at $\kappa$ and obeying the constraints of Easton's theorem, namely, $F(\alpha)\leq F(\beta)$ for $\alpha\leq\beta$ and $\alpha<\cf(F(\alpha))$, then there is a cofinality preserving forcing extension in which $\kappa$ remains Ramsey or strongly Ramsey respectively and $2^\delta=F(\delta)$ for every regular cardinal $\delta$.