2021/01/04 by Farmer Schlutzenberg, Schlutzenberg, Farmer
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #03E45 #03E55 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Receptor Mechanisms and Signaling
paper · pdf · doi:10.48550/arxiv.2101.00889
openalex publication_date 2021/01/04 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let M be a λ-indexed (that is, Jensen indexed) premouse. We prove that M is iterable with respect to standard λ-iteration rules iff M is iterable with respect to a natural version of Mitchell-Steel iteration rules. Using this equivalence, we describe a background construction for λ-indexed mice, analogous to traditional background constructions for Mitchell-Steel indexed mice, and which absorbs Woodin cardinals from the background universe. We also prove some facts regarding the correspondence between standard iteration trees and u-iteration trees on premice with Mitchell-Steel indexing.