Superclub, splitting, separating statements

2023/02/02 by Shimon Garti, Saharon Shelah, Garti, Shimon +1
Computer Science · Mathematics · #03E02 #03E17 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2302.00904

openalex publication_date 2023/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that superclub implies \mathfraks=ℵ₁. More generally, superclub at a successor of a weakly compact cardinal implies \mathfraks_κ=κ⁺. Based on this statement, we separate tiltan from superclub at a successor of a supercompact cardinal. We use Galvin's property in order to separate tiltan from superclub at successors of both regular and singular cardinals.

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