Cichon's Diagram for uncountable cardinals

2016/11/24 by Joerg Brendle, Andrew Brooke-Taylor, Brendle, Joerg +5 · 3 citations
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.1611.08140

arxiv created 2016/11/24 · arxiv updated 2016/11/28

Abstract

We develop a version of Cichon's diagram for cardinal invariants on the generalized Cantor space 2^kappa or the generalized Baire space kappa^kappa where kappa is an uncountable regular cardinal. For strongly inaccessible kappa, many of the ZFC-results about the order relationship of the cardinal invariants which hold for omega generalize; for example we obtain a natural generalization of the Bartoszynski-Raisonnier-Stern Theorem. We also prove a number of independence results, both with <kappa-support iterations and kappa-support iterations and products, showing that we consistently have strict inequality between some of the cardinal invariants.

Cited by

• Eventual Capture on a Measurable Cardinal
• Dominating numbers at singular cardinals
• Laver Trees in the Generalized Baire Space
• Forcing Diamond and Applications to Iterability

Related

• Higher Dimensional Cardinal Characteristics for Sets of Functions
• The higher Cichon diagram in the degenerate case
• The Horizontal Direction
• Two results on cardinal invariants at uncountable cardinals
• Alternative Cichoń Diagrams and Forcing Axioms Compatible with CH