2023/08/01 by Assaf Rinot, Rinot, Assaf, Shira Yadai +3 · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Primary 03E05. Secondary 03E35 #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2308.00299
openalex publication_date 2023/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A κ-tree is said to be full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full κ-Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal. Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be ℵ3 many full ℵ2-trees such that the product of any countably many of them is an ℵ2-Souslin tree.