2020/01/05 by Toshimichi Usuba, Usuba, Toshimichi
Computer Science · Mathematics · #03E55 #54A25 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2001.02124
openalex publication_date 2020/01/05 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper we investigate more characterizations and applications of δ-strongly compact cardinals. We show that, for a cardinal κ the following are equivalent: (1) κ is δ-strongly compact, (2) For every regular λ≥ κ there is a δ-complete uniform ultrafilter over λ, and (3) Every product space of δ-Lindelöf spaces is κ-Lindelöf. We also prove that in the Cohen forcing extension, the least ω1-strongly compact cardinal is a precise upper bound on the tightness of the products of two countably tight spaces.