2022/12/06 by Yair Hayut, Hayut, Yair, Alejandro Poveda +1 · 1 citation
Computer Science · Mathematics · #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.2212.03333
openalex publication_date 2022/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new compactness principle which we call the gluing property. For a measurable cardinal κ and a cardinal λ, we say that κ has the λ-gluing property if every sequence of λ-many κ-complete ultrafilters on κ can be glued into a κ-complete extender. We show that every κ-compact cardinal has the 2κ-gluing property, yet non-necessarily the (2κ)+-gluing property. Finally, we compute the exact consistency-strength for κ to have the ω-gluing property; this being o(κ)=ω1.