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Distributivity and base trees for $P(\kappa)/ {\lt} \kappa$
Published online by Cambridge University Press: 07 May 2024
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 $.
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society