Corpus ID: 221703357

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

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


    Publications referenced by this paper.
    Killing them softly: degrees of inaccessible and Mahlo cardinals
    • 1
    The Set-Theoretic Multiverse
    • 77
    • PDF
    Pointwise definable models of set theory
    • 17
    • PDF
    Resurrection axioms and uplifting cardinals
    • 22
    • PDF
    Informal Rigour and Completeness Proofs
    • 265
    Believing the Axioms I
    • P. Maddy
    • Mathematics, Computer Science
    • 1988
    • 130
    • PDF
    Believing the axioms, I. The Journal of Symbolic Logic
    • 1988