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/