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  1. Maximality Principles in the Hyperuniverse Programme.Sy-David Friedman & Claudio Ternullo - forthcoming - Foundations of Science:1-19.
    In recent years, one of the main thrusts of set-theoretic research has been the investigation of maximality principles for V, the universe of sets. The Hyperuniverse Programme has formulated several maximality principles, which express the maximality of V both in height and width. The paper provides an overview of the principles which have been investigated so far in the programme, as well as of the logical and model-theoretic tools which are needed to formulate them mathematically, and also briefly shows how (...)
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  • Ideal Objects for Set Theory.Santiago Jockwich, Sourav Tarafder & Giorgio Venturi - 2022 - Journal of Philosophical Logic 51 (3):583-602.
    In this paper, we argue for an instrumental form of existence, inspired by Hilbert’s method of ideal elements. As a case study, we consider the existence of contradictory objects in models of non-classical set theories. Based on this discussion, we argue for a very liberal notion of existence in mathematics.
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