# Categorical large cardinals and the tension between categoricity and set-theoretic reflection

@article{Hamkins2020CategoricalLC, title={Categorical large cardinals and the tension between categoricity and set-theoretic reflection}, author={J. D. Hamkins and Hans Robin Solberg}, journal={arXiv: Logic}, year={2020} }

Inspired by Zermelo's quasi-categoricity result characterizing the models of second-order Zermelo-Fraenkel set theory $\text{ZFC}_2$, we investigate when those models are fully categorical, characterized by the addition to $\text{ZFC}_2$ either of a first-order sentence, a first-order theory, a second-order sentence or a second-order theory. The heights of these models, we define, are the categorical large cardinals. We subsequently consider various philosophical aspects of categoricity for… CONTINUE READING

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