Forcing constellations of Cichoń's diagram by using the Tukey order

2022/03/01 by Miguel A. Cardona, Cardona, Miguel A., Diego A. Mejía +1 · 1 citation
Computer Science · #03E17 #03E35 #03E40 #FOS: Mathematics #Logic (math.LO) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2203.00615

openalex publication_date 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use known finite support iteration techniques to present various examples of models where several cardinal characteristics of Cichoń's diagram are pairwise different. We show some simple examples forcing the left-hand side of Cichoń's diagram, and present the technique of restriction to models to force Cichoń's maximum (original from Goldstern, Kellner, Shelah, and the second author). We focus on how the values forced in all the constellations are obtained via the Tukey order.

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