On strong forms of reflection in set theory
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.
Honzik, R. (2018)., On strong forms of reflection in set theory, in C. Antos, R. Honzik, C. Ternullo & S. D. Friedman (eds.), The hyperuniverse project and maximality, Dordrecht, Springer, pp. 125-134.
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