2023/06/24 by Farmer Schlutzenberg, Schlutzenberg, Farmer
Mathematics · #03E45 #03E55 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2306.13827
openalex publication_date 2023/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We give a development of the fine structure of mice with long extenders, to the level of κ+-supercompact cardinals κ. We do this using a hierarchy with features more analogous to those familiar in the short extender context than the hierarchies introduced by Woodin and by Neeman-Steel. In particular, the mice we consider satisfy stronger versions of the initial segment condition. We establish a form of fine structural condensation involving embeddings π:H→ M which need not be the identity below the projectum of H (under special assumptions). We also adapt the analysis of the Dodd structure of short extenders on the sequence to mice at this level.