A Strong Reflection Principle

Roberts, Sam

A Strong Reflection Principle

Dateien

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Datum

2017

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Philosophie

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

The Review of Symbolic Logic. Cambridge University Press. 2017, 10(4), pp. 651-662. ISSN 1755-0203. eISSN 1755-0211. Available under: doi: 10.1017/S1755020317000223

Zusammenfassung

This article introduces a new reflection principle. It is based on the idea that whatever is true in all entities of some kind is also true in a set-sized collection of them. Unlike standard reflection principles, it does not re-interpret parameters or predicates. This allows it to be both consistent in all higher-order languages and remarkably strong. For example, I show that in the language of second-order set theory with predicates for a satisfaction relation, it is consistent relative to the existence of a 2-extendible cardinal (Theorem 7.12) and implies the existence of a proper class of 1-extendible cardinals (Theorem 7.9).

Fachgebiet (DDC)

100 Philosophie

Schlagwörter

set theory, reflection principles, large cardinals, intrinsic justification

Zitieren

ISO 690

ROBERTS, Sam, 2017. A Strong Reflection Principle. In: The Review of Symbolic Logic. Cambridge University Press. 2017, 10(4), pp. 651-662. ISSN 1755-0203. eISSN 1755-0211. Available under: doi: 10.1017/S1755020317000223

BibTex

@article{Roberts2017Stron-53567,
  year={2017},
  doi={10.1017/S1755020317000223},
  title={A Strong Reflection Principle},
  number={4},
  volume={10},
  issn={1755-0203},
  journal={The Review of Symbolic Logic},
  pages={651--662},
  author={Roberts, Sam}
}

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