2008/06/26 by James Hirschorn, Hirschorn, James
Computer Science · Mathematics · #03E05 #03E15 #03E35 (Primary) #03E50 (Secondary) #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #msc:03E05 #msc:03E15 #msc:03E35 #msc:03E50
paper · pdf · doi:10.48550/arxiv.0806.4220
54 pages (Elsevier article style). To appear in Annals of Pure and Applied Logic. Homepage: http://homepage.univie.ac.at/James.Hirschorn/research/strong.antidiamond/strong.antidiamond.html
arxiv created 2008/06/26 · openalex publication_date 2008/06/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A strong antidiamond principle (*c) is shown to be consistent with CH. This principle can be stated as a "P-ideal dichotomy": every P-ideal on omega-1 (i.e. an ideal that is sigma-directed under inclusion modulo finite) either has a closed unbounded subset of omega-1 locally inside of it, or else has a stationary subset of omega-1 orthogonal to it. We rely on Shelah's theory of parameterized properness for NNR iterations, and make a contribution to the theory with a method of constructing the properness parameter simultaneously with the iteration. Our handling of the application of the NNR iteration theory involves definability of forcing notions in third order arithmetic, analogous to Souslin forcing in second order arithmetic.