CichoA''s diagram for uncountable cardinals

摘要

We develop a version of CichoA"'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 BartoszyA"ski-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.