Publikation:

Are Large Cardinal Axioms Restrictive?

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2023

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https://doi.org/10.1093/philmat/nkad014
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Austrian Science Fund (FWF): P 28420

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Philosophia Mathematica. Oxford University Press (OUP). 2023, 31(3), S. 372-407. ISSN 0031-8019. eISSN 1744-6406. Verfügbar unter: doi: 10.1093/philmat/nkad014

Zusammenfassung

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim. I show that there is a kind of maximality (namely absoluteness) on which large cardinal axioms come out as restrictive relative to a formal notion of restrictiveness. Within this framework, I argue that large cardinal axioms can still play many of their usual foundational roles.

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100 Philosophie

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ISO 690BARTON, Neil, 2023. Are Large Cardinal Axioms Restrictive?. In: Philosophia Mathematica. Oxford University Press (OUP). 2023, 31(3), S. 372-407. ISSN 0031-8019. eISSN 1744-6406. Verfügbar unter: doi: 10.1093/philmat/nkad014
BibTex
@article{Barton2023-10-15Large-75969,
  title={Are Large Cardinal Axioms Restrictive?},
  year={2023},
  doi={10.1093/philmat/nkad014},
  number={3},
  volume={31},
  issn={0031-8019},
  journal={Philosophia Mathematica},
  pages={372--407},
  author={Barton, Neil}
}
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