1997/02/18 by Ernest Schimmerling, Schimmerling, Ernest, John R. Steel +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO
paper · pdf · doi:10.48550/arxiv.math/9702206
arxiv created 1997/02/18 · openalex publication_date 1997/02/18 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K computes successors of weakly compact cardinals correctly. o Kc is an iterate of K. o (with Mitchell) If alpha is a cardinal > aleph1, then K-restriction-alpha is universal for mice of height alpha. Other results in this paper, when combined with work of Woodin, imply: o If square-kappa-finite fails and kappa is a singular, strong limit cardinal, then Inductive Determinacy holds. o If square-kappa-finite fails and kappa is a weakly compact cardinal, then L(R)-determinacy holds.