The Search for New Axioms in the Hyperuniverse Programme

Sy-David Friedman, Claudio Ternullo

    Veröffentlichungen: Beitrag in BuchBeitrag in Buch/SammelbandPeer Reviewed

    Abstract

    The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the ‘maximal iterative concept’, and the programme identifies higher-order statements motivated by the maximal iterative concept. The satisfaction of these statements ($$\mathbb {H}$$ -axioms) in countable transitive models, the collection of which constitutes the ‘hyperuniverse’ ($$\mathbb {H}$$ ), has remarkable first-order consequences, some of which we review in Sect. 10.5.

    OriginalspracheEnglisch
    TitelObjectivity, Realism, and Proof
    Redakteure*innenF. Boccuni, A. Sereni
    ErscheinungsortCham
    Herausgeber (Verlag)Springer
    Seiten165-188
    Seitenumfang24
    ISBN (elektronisch)978-3-319-31644-4
    ISBN (Print)978-3-319-31642-0
    DOIs
    PublikationsstatusVeröffentlicht - Juli 2016

    Publikationsreihe

    ReiheBoston Studies in the Philosophy and History of Science
    Band318
    ISSN0068-0346

    ÖFOS 2012

    • 101013 Mathematische Logik

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