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On Strong Forms of Reflection in Set Theory

In: The Hyperuniverse Project and Maximality

Author

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  • Sy-David Friedman

    (Universität Wien, Kurt Gödel Research Center for Mathematical Logic)

  • Radek Honzik

    (Universität Wien, Kurt Gödel Research Center for Mathematical Logic)

Abstract

In this paper we review the most common forms of reflection and introduce a new form which we call sharp-generated reflection. We argue that sharp-generated reflection is the strongest form of reflection which can be regarded as a natural generalization of the Lévy reflection theorem. As an application we formulate the principle sharp-maximality with the corresponding hypothesis IMH # . IMH # is an analogue of the IMH (Inner Model Hypothesis, introduced in Friedman (Bull Symb Log 12(4):591–600, 2006)) which is compatible with the existence of large cardinals.

Suggested Citation

  • Sy-David Friedman & Radek Honzik, 2018. "On Strong Forms of Reflection in Set Theory," Springer Books, in: Carolin Antos & Sy-David Friedman & Radek Honzik & Claudio Ternullo (ed.), The Hyperuniverse Project and Maximality, pages 125-134, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-62935-3_6
    DOI: 10.1007/978-3-319-62935-3_6
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