The core model for almost linear iterations

2000/02/11 by Ralf-Dieter Schindler, Ralf‐Dieter Schindler, Schindler, Ralf-Dieter
Mathematics · Medicine · #03E15 #03E45 #03E55 #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #Neurological and metabolic disorders #math.LO #msc:03E15 #msc:03E45 #msc:03E55

paper · pdf · doi:10.48550/arxiv.math/0002089

80 pages

openalex publication_date 2000/02/11 · arxiv created 2001/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce 0^h (0^handgrenade) as a sharp for an inner model with a proper class of strong cardinals. If 0^h does not exist then any normal iteration tree is "almost linear." We exploit this fact to prove the existence of the core model K in the theory "ZFC + 0^h does not exist." (As of today, non-0^h is thereby the weakest anti large cardinal assumption under which K can be shown to exist in ZFC. In this sense we improve earlier work of Dodd, Jensen, Mitchell, and - partially - Steel.) We indicate that our paper provides the last step for determining the exact consistency strength of a statement in the Delfino problem list.

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