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We provide a model where u(κ) < 2^κ for a supercompact cardinal κ.  provides a sketch of how to obtain such a model by modifying the construction in . We provide here a complete proof using a different modification of  and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties.
- Generalized cardinal characteristics
- Supercompact cardinals
Brooke-Taylor, A. D., Fischer, V., Friedman, S-D., & Montoya, D. (2017). Cardinal characteristics at κ in a small u(κ) model. Annals of Pure and Applied Logic, 168(1), 37–49. https://doi.org/10.1016/j.apal.2016.08.004