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Document Details : Title: Irreducible Features of Set Theories Author(s): FREIRE, Alfredo Roque Journal: Logique et Analyse Volume: 262 Date: 2023 Pages: 95-123 DOI: 10.2143/LEA.262.0.3293615 Abstract : The universalist position in set theory maintains that there is just one maximal universe of sets. It maintains that all sentences about sets in that universe are either true or false. In practice, however, set theorists investigate a myriad of alternative structures, hence a universalist who does not wish to simply dismiss the diversity of mathematical practice must somehow account for those alternative structures. It is unclear how the universalist would do so without relying upon interpretations of those alternative universes in a base universe. Indeed, this seems a core feature of universalism itself. Nonetheless, recent results on set-theoretic interpretations in set theories by Enayat, and by Freire and Hamkins, put serious limitations on the universalist’s ability to produce such interpretations. The universalist, we argue, thus cannot account for the real diversity of mathematical practice. |
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