Easton's theorem for Ramsey and strongly Ramsey cardinals

Abstract

We show that, assuming GCH, if κ is a Ramsey or a strongly Ramsey cardinal and F is a class function on the regular cardinals having a closure point at κ and obeying the constraints of Easton’s theorem, namely, F (α) ≤ F (β) for α ≤ β and α < cf(F (α)), then there is a cofinality preserving forcing extension in which κ remains Ramsey or strongly Ramsey respectively and 2δ = F (δ) for every regular cardinal δ.

DOI: 10.1016/j.apal.2015.04.006

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Cite this paper

@article{Cody2015EastonsTF, title={Easton's theorem for Ramsey and strongly Ramsey cardinals}, author={Brent Cody and Victoria Gitman}, journal={Ann. Pure Appl. Logic}, year={2015}, volume={166}, pages={934-952} }