Easton's theorem for Ramsey and strongly Ramsey cardinals

摘要

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) <= F(beta) for alpha <= 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. (C) 2015 Elsevier B.V. All rights reserved.