Plural Frege Arithmetic

In [Boccuni 2010], a predicative fragment of Frege’s BLV augmented with Boolos’ unrestricted plural quantification is shown to interpret PA2. The main disadvantage of that axiomatisation is that it does not recover Frege Arithmetic FA because of the restrictions imposed on the axioms. The aim of the present article is to show how [Boccuni 2010] can be consistently extended so as to interpret FA and consequently PA2 in a way that parallels Frege’s. In that way, the presented system will be compared with the system PE in [Ferreira 2018] and some relevant differences between the two will be highlighted.