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?



Short proof of $\frak p=t$
One reference is given above by Inamdar that can be found here:


[$\frak p=t$, following Malliaris-Shelah and Steprans](https://www1.essex.ac.uk/maths/people/fremlin/n14528.pdf) ([Internet Archive](http://web.archive.org/web/20180605111554/https://www1.essex.ac.uk/maths/people/fremlin/n14528.pdf)).


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](http://www.logicatorino.altervista.org/matteo_viale/tesi-moranarocca.pdf) ([Internet Archive](http://web.archive.org/web/20180605111721/http://www.logicatorino.altervista.org/matteo_viale/tesi-moranarocca.pdf))


