Large cardinals as principles of Structural Reflection

Joan Bagaria

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arXiv · 2107.01580

Large cardinals as principles of Structural Reflection

Joan Bagaria

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Abstract

After discussing the limitations inherent to all set-theoretic reflection principles akin to those studied by A. L\'evy et. al. in the 1960's, we introduce new principles of reflection based on the general notion of \emph{Structural Reflection} and argue that they are in strong agreement with the conception of reflection implicit in Cantor's original idea of the unknowability of the \emph{Absolute}, which was subsequently developed in the works of Ackermann, L\'evy, G\"odel, Reinhardt, and others. We then present a comprehensive survey of results showing that different forms of the new principles of Structural Reflection are equivalent to well-known large cardinals axioms covering all regions of the large-cardinal hierarchy, thereby justifying the naturalness of the latter.

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BibTeX RIS

Joan Bagaria. 2021-07-04. Large cardinals as principles of Structural Reflection. https://arxiv.org/abs/2107.01580

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