On Strong Forms of Reflection in Set Theory

Sy-David Friedman () and Radek Honzik ()
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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

A chapter in The Hyperuniverse Project and Maximality, 2018, pp 125-134 from Springer

Abstract: 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-62935-3_6

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DOI: 10.1007/978-3-319-62935-3_6

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