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Explaining Maximality Through the Hyperuniverse Programme

In: The Hyperuniverse Project and Maximality

Author

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  • Sy-David Friedman

    (University of Vienna, Kurt Gödel Research Center for Mathematical Logic)

  • Claudio Ternullo

    (University of Vienna, Kurt Gödel Research Center for Mathematical Logic)

Abstract

The (maximal) iterative concept of set is standardly taken to justify ZFC and some of its extensions. In this paper, we show that the maximal iterative concept also lies behind a class of further maximality principles expressing the maximality of the universe of sets V in height and width. These principles have been heavily investigated by the first author and his collaborators within the Hyperuniverse Programme. The programme is based on two essential tools: the hyperuniverse, consisting of all countable transitive models of ZFC, and V -logic, both of which are also fully discussed in the paper.

Suggested Citation

  • Sy-David Friedman & Claudio Ternullo, 2018. "Explaining Maximality Through the Hyperuniverse Programme," Springer Books, in: Carolin Antos & Sy-David Friedman & Radek Honzik & Claudio Ternullo (ed.), The Hyperuniverse Project and Maximality, pages 185-204, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-62935-3_9
    DOI: 10.1007/978-3-319-62935-3_9
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