Small u_kappa and large 2^kappa for supercompact kappa

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.