2021/07/13 by Jörg Brendle, Brendle, Jörg, Corey Bacal Switzer +1
Computer Science · Mathematics · #03E17 #03E35 #03E50 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2107.05947
openalex publication_date 2021/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the values of the higher dimensional cardinal characteristics for sets of functions f:ωω→ ωω introduced by the second author. We prove that while the bounding numbers for these cardinals can be strictly less than the continuum, the dominating numbers cannot. We compute the bounding numbers for the higher dimensional relations in many well known models of \negCH such as the Cohen, random and Sacks models and, as a byproduct show that, with possibly one exception, for the bounding numbers there are no ZFC relations between them beyond those in the higher dimensional Cichoń diagram. In the case of the dominating numbers we show that in fact they collapse in the sense that modding out by the ideal does not change their values. Moreover, they are closely related to the dominating numbers \mathfrakdλκ.