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, $F(\alpha )\le F(\beta )$ for $\alpha \le \beta$ and $α<\cf(F(α))$, 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 $\delta$.

21 pages

References in corpus (1)

• Some results on large cardinals and the continuum function