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Distributivity and base trees for $P(\kappa)/ {\lt} \kappa$

Part of: Set theory

Published online by Cambridge University Press:  07 May 2024

Geoff Galgon
Geoff Galgon*
Affiliation:
Independent, Philadelphia, PA, United States
*
e-mail: geoff@nimbus.solar
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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 $.

Keywords

Distributivity matrixdistributivity treetree of maximal antichainsgeneralized Baire space

MSC classification

Primary: 03E05: Other combinatorial set theory
Secondary: 03E17: Cardinal characteristics of the continuum
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 12
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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References

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