Distributivity and base trees for

Abstract

Abstract For $\kappa $ a regular uncountable cardinal, we show that distributivity and base trees for $P(\kappa )/{<}\kappa $ of intermediate height in the cardinal interval $[\omega , \kappa )$ exist in certain models. We also show that base trees of height $\kappa $ can exist as well as base trees of various heights $\geq \kappa ^+$ depending on the spectrum of cardinalities of towers in $P(\kappa )/{<}\kappa $ .