2021/10/22 by Grigor Sargsyan, Sargsyan, Grigor, Ralf Schindler +3
Computer Science · Mathematics · #03E40 #03E45 #03E55 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2110.12051
openalex publication_date 2021/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assume the existence of sufficent large cardinals. Let Mswn be the minimal iterable proper class L[E] model satisfying "there are δ0<κ0<…<δn-1<κn-1 such that the δi are Woodin cardinals and the κi are strong cardinals". Let M=Msw2. We identify an inner model \mathscrV2M of M, which is a proper class model satisfying "there are 2 Woodin cardinals", and is iterable both in V and in M, and closed under its own iteration strategy. The construction also yields significant information about the extent to which M knows its own iteration strategy. We characterize the universe of \mathscrV2M as the mantle and the least ground of M, and as HODM[G] for G\subseteqColl(ω,λ) being M-generic with λ sufficiently large. These results correspond to facts already known for Msw1, and the proofs are an elaboration of those, but there are substantial new issues and new methods used to handle them.