Small u_kappa and large 2^kappa for supercompact kappa
Andrew D. Brooke-Taylor

TL;DR
This paper explains how to use forcing techniques to make the minimal size of a certain ideal at a supercompact cardinal equal to its successor while making the continuum arbitrarily large.
Contribution
It provides detailed exposition on forcing methods to achieve specific set-theoretic configurations at supercompact cardinals, extending prior results.
Findings
u_kappa can be forced to be kappa^+
2^kappa can be made arbitrarily large
Detailed forcing construction provided
Abstract
In a recent preprint, Garti and Shelah state that the techniques of a paper of Dzamonja and Shelah can be used to force u_kappa to be kappa^+ for supercompact kappa with 2^kappa arbitrarily large. In this expository article we spell out the details of how this can be done.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsBlack Holes and Theoretical Physics · Noncommutative and Quantum Gravity Theories · Algebraic structures and combinatorial models
