Universal graphs between a strong limit singular and its power

2022/01/03 by Márk Poór, Saharon Shelah, Poór, Márk +1
Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2201.00741

Abstract

The paper settles the problem of the consistency of the existence of a single universal graph between a strong limit singular and its power. Assuming that in a model of GCH κ is supercompact and the cardinals θ < κ, λ > κ are regular, as an application of a more general method we obtain a forcing extension in which \textrmcf(κ) = θ, the Singular Cardinal Hypothesis fails at κ and there exists a universal graph in cardinality λ ∈ (κ,2^κ).

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