November 8
Geoff Galgon,
Distributivity and Base trees for $P(\kappa)/ {\lt} \kappa$
For $\kappa$ a regular uncountable cardinal, we show that distributivity and base trees for $P(\kappa)/{\lt}\kappa$ 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 $P(\kappa)/{\lt}\kappa$. These constructions answer questions of V. Fischer, M. Koelbing, and W. Wohofsky in certain models.