Easton's Theorem for Ramsey and Strongly Ramsey cardinals

2012/09/05 by Brent Cody, Cody, Brent, Victoria Gitman +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Mathematical and Theoretical Analysis #math.LO #msc:03E35 #msc:03E55

paper · pdf · doi:10.48550/arxiv.1209.1133

21 pages

arxiv created 2012/09/05 · arxiv updated 2012/09/07

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 2^δ=F(δ) for every regular cardinal δ.

Related

• Easton's Theorem in the presence of Woodin cardinals
• Easton functions and supercompactness
• Some results on large cardinals and the continuum function
• An Easton like theorem in the presence of Shelah Cardinals
• Ramsey-like cardinals II