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  1. Does Set Theory Really Ground Arithmetic Truth?Alfredo Roque Freire - manuscript
    We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to emphasize the incomplete picture of both theories and treat models as their syntactical counterparts. Insisting on the incomplete picture will allow us to argue in favor of the revisability of the standard model interpretation. We then show that it is hopeless to expect that the (...)
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  • The Ontological Import of Adding Proper Classes.Alfredo Roque Freire & Rodrigo de Alvarenga Freire - 2019 - Manuscrito 42 (2):85-112.
    In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of (...)
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