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The Search for New Axioms in the Hyperuniverse Programme

In: The Hyperuniverse Project and Maximality

Author

Listed:
  • 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 Hyperuniverse Programme, introduced in Arrigoni and Friedman (Bull Symb Log 19(1):77–96, 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 ( ℍ $$\mathbb {H}$$ -axioms) in countable transitive models, the collection of which constitutes the ‘hyperuniverse’ ( ℍ $$\mathbb {H}$$ ), has remarkable first-order consequences, some of which we review in Sect. 5.

Suggested Citation

  • Sy-David Friedman & Claudio Ternullo, 2018. "The Search for New Axioms in the Hyperuniverse Programme," Springer Books, in: Carolin Antos & Sy-David Friedman & Radek Honzik & Claudio Ternullo (ed.), The Hyperuniverse Project and Maximality, pages 161-183, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-62935-3_8
    DOI: 10.1007/978-3-319-62935-3_8
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