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Distributivity and base trees for
$P(\kappa)/ {\lt} \kappa$
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 4 / December 2024
- Published online by Cambridge University Press:
- 07 May 2024, pp. 915-926
- Print publication:
- December 2024
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- Article
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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 $.
