Large cardinals as principles of Structural Reflection
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.
Keywords
Cite
@article{arxiv.2107.01580,
title = {Large cardinals as principles of Structural Reflection},
author = {Joan Bagaria},
journal= {arXiv preprint arXiv:2107.01580},
year = {2021}
}