2012/07/24 by Brent Cody, Cody, Brent
Computer Science · Mathematics · #03E35 #03E55 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03E35 #msc:03E55
paper · pdf · doi:10.48550/arxiv.1207.5822
22 pages
openalex publication_date 2012/07/24 · arxiv created 2012/07/27 · arxiv updated 2012/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Under the assumption that δ is a Woodin cardinal and \GCH holds, I show that if F is any class function from the regular cardinals to the cardinals such that (1) κ<\cf(F(κ)), (2) κ<λ implies F(κ)≤ F(λ), and (3) δ is closed under F, then there is a cofinality-preserving forcing extension in which 2γ= F(γ) for each regular cardinal γ<δ, and in which δ remains Woodin. Unlike the analogous results for supercompact cardinals [Men76] and strong cardinals [FH08], there is no requirement that the function F be locally definable.