Notes

Miscellaneous notes I’ve written, usually for my own benefit, as some things can be hard to find in the published literature. Hopefully, someone else finds them useful. More notes will be added eventually.

These have not been carefully proof-read, so please let me know if you find any mistakes.

• Kaplansky’s conjecture. This is an exposition of Woodin’s proof of the consistency of “Every algebra morphism from $C(X)$ to a Banach algebra is automatically continuous”, assuming Woodin’s condition as a black box. I’ll eventually add the Banach algebra theory that is necessary to deduce Woodin’s condition.
• Cardinal functions in topology. Some notes from a talk I gave at the graduate student set theory and model theory seminar at CMU.