On strong forms of reflection in set theory

Mathematical Logic Quarterly 62 (1-2):52-58 (2016)
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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. The statement is an analogue of the (Inner Model Hypothesis, introduced in ) which is compatible with the existence of large cardinals.

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Universism and extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - 2021 - Review of Symbolic Logic 14 (1):112-154.
Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.

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References found in this work

On reflection principles.Peter Koellner - 2009 - Annals of Pure and Applied Logic 157 (2-3):206-219.
Internal consistency and the inner model hypothesis.Sy-David Friedman - 2006 - Bulletin of Symbolic Logic 12 (4):591-600.

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