2020/09/03 by Yurii Khomskii, Khomskii, Yurii, Marlene Koelbing +5
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.2009.01886
arxiv created 2020/09/03 · openalex publication_date 2020/09/03 · arxiv updated 2020/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that any suitable generalization of Laver forcing to the space κκ, for uncountable regular κ, necessarily adds a Cohen κ-real. We also study a dichotomy and an ideal naturally related to generalized Laver forcing. Using this dichotomy, we prove the following stronger result: if κ<κ=κ, then every <κ-distributive tree forcing on κκ adding a dominating κ-real which is the image of the generic under a continuous function in the ground model, adds a Cohen κ-real. This is a contribution to the study of generalized Baire spaces and answers a question from arXiv:1611.08140