1994/07/12 by Andreas Blass, Blass, Andreas
Mathematics · #FOS: Mathematics #Logic (math.LO) #Mathematics and Applications #math.LO
paper · pdf · doi:10.48550/arxiv.math/9407203
arxiv created 1994/07/12 · openalex publication_date 1994/07/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss two general aspects of the theory of cardinal characteristics of the continuum, especially of proofs of inequalities between such characteristics. The first aspect is to express the essential content of these proofs in a way that makes sense even in models where the inequalities hold trivially (e.g., because the continuum hypothesis holds). For this purpose, we use a Borel version of Vojtas's theory of generalized Galois-Tukey connections. The second aspect is to analyze a sequential structure often found in proofs of inequalities relating one characteristic to the minimum (or maximum) of two others. Vojtas's max-min diagram, abstracted from such situations, can be described in terms of a new, higher-type object in the category of generalized Galois-Tukey connections. It turns out to occur also in other proofs of inequalities where no minimum (or maximum) is mentioned.