Hm, I thought with type-level exponentiation that I'd be able to easily define, and prove the existence of, very large Beth numbers. It turns out I really don't get how to talk about cardinals in NF+Counting/ML+N.
For one, I don't even know how I'd define beth_omega, much less prove (as I would need to) that it is Tc for some cardinal c. I mean, outside of invoking it as a supremum that might not exist in these set theories. Forster explained part of the solution to this, but not enough that I can piece the details together.
I dislike feeling like I need my hand held on things like this.