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On strong forms of reflection in set theory

Publication at Faculty of Arts |
2016

Abstract

In this paper we review the most common forms of reflection and introduce a new form which we call \emph{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 Levy reflection theorem.

As an application we formulate the principle \emph{sharp-maximality} with the corresponding hypothesis IMH$^\#$. IMH$^\#$ is an analogue of the IMH (Inner Model Hypothesis which is compatible with the existence of large cardinals.