The Horizontal Direction

2025/03/06 by T. van der Vlugt, van der Vlugt, Tristan
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2503.04471

Abstract

We give a survey of cardinal charcteristics of the higher Cichoń diagram defined on the higher Baire space ^κκ for κ regular with 2^<κ=κ. Specifically, we will compare consistency proofs from the classical Cichoń diagram with various well-known forcing notions to similar constructions generalised to the higher Cichoń diagram. We are especially interested in separation in a horizontal direction, that is, the consistency of add(\mathcal M_κ)<non(\mathcal M_κ) and of cov(\mathcal M_κ)<cof(\mathcal M_κ). We will have a look at (higher analogues of) Cohen, Hechler, localisation, eventually different, Sacks, random, Laver, Mathias and Miller forcing, and their effect on the cardinal characteristics of the higher Cichoń diagram.

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