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arXiv · 1611.08140

Cichon's Diagram for uncountable cardinals

Joerg Brendle·Andrew Brooke-Taylor·Sy-David Friedman·Diana Montoya
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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.

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Joerg Brendle, Andrew Brooke-Taylor, Sy-David Friedman, Diana Montoya. 2016-11-24. Cichon's Diagram for uncountable cardinals. https://arxiv.org/abs/1611.08140

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