Mice with Woodin cardinals from a Reinhardt

2024/02/06 by Farmer Schlutzenberg, Schlutzenberg, Farmer
Mathematics · #03E25 #03E45 #03E55 #03E60 #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2402.04065

openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose there is a Reinhardt cardinal. Then (1) M_n(X) exists and is fully iterable (above X) for every transitive set X and every n<ω (here M_n(X) denotes the canonical minimal proper class inner model containing X and having n Woodin cardinals above the rank of X); and (2) Projective Determinacy holds in every set generic extension.

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