Global Square and Mutual Stationarity at the Aleph_n

2007/09/26 by Peter Koepke, Koepke, Peter, Philip Welch +1
Computer Science · Mathematics · #03E10 #03E35 #03E45 #03E55 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Theory of Mathematics #Logic (math.LO) #math.LO #msc:03E10 #msc:03E35 #msc:03E45 #msc:03E55

paper · pdf · doi:10.48550/arxiv.0709.4127

34 pages

arxiv created 2007/09/26 · openalex publication_date 2007/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show using a proof of the Global Square property in Core Models below a measurable of Mitchell order o(kappa)=kappa⁺+ (a result originally due to Jensen & Zeman) that Foreman and Magidor's Mutual Stationarity property MS(Aleph_n (1<n<omega), Cof(omega₁)) implies the existence of inner models with measurables of high Mitchell order. This MS property states that any sequence of independently chosen stationary subsets S_n of the Aleph_n (of fixed cofinality omega₁) is mutually stationary below aleph_omega.

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