[FOM] Collecting independence results

[Daniel Ian Rosenbloom]

Dear FOMers,

For my undergraduate thesis, I'm considering doing a project on
independence results in set theory that have applications to other areas
of mathematics.  To that end, I am searching for any such results that
exist scattered across articles and would benefit from a more
consolidated/general/modern/detailed exposition and/or results that are of
great general interest to mathematicians.  So far, I'm looking at
Whitehead's conjecture, Kaplansky's conjecture, and Shelah and Soifer's
work on AC and chromatic numbers of the plane, but I want to find more.

Would anyone have references to other results that I could use?  I'd
greatly appreciate any help.

Sincerely,
Daniel Rosenbloom