We prove the results stated in the title.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-2-2,
author = {Hiroshi Sakai},
title = {Partial square at o1 is implied by MM but not by PFA},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {109-131},
zbl = {1244.03126},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-2-2}
}
Hiroshi Sakai. Partial square at ω₁ is implied by MM but not by PFA. Fundamenta Mathematicae, Tome 215 (2011) pp. 109-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-2-2/