It is known for a while now that $\frak p=t$, as a result of Malliaris-Shelah. The original paper draws from model theoretic methods.
I've heard rumors that there was a proof which was purely set theoretic, and indeed much shorter than the original.
Does anyone know who wrote it, and whether or not it appears online/in print, and if so, is there an available link/reference?
One reference is given above by Inamdar that can be found here:
$\frak p=t$, following Malliaris-Shelah and Steprans (Internet Archive).
Also there is another reference where not only it gives a proof of the $\frak p=t$ based on Steprans ideas, but it also gives in a very nice way some other results proved by Malliaris-Shelah:
Ultraproducts of finite partial orders and some of their applications in model theory and set theory (Internet Archive)
While not short, A Measure Theoretic Proof of $\mathfrak p=\mathfrak t$ gives a proof that does not rely on model theoretic or proof theoretic techniques. Since the measure theory is basic, Kunen's text is sufficient background. (It in fact establishes a stronger result which implies the equality.)
To my knowledge, all of the other proofs are distillations of the original Malliaris--Shelah proof.
