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A STRONG REFLECTION PRINCIPLE

  • SAM ROBERTS

Abstract

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).

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*DEPARTMENT OF PHILOSOPHY IFIKK UNIVERSITY OF OSLO POSTBOKS 1020 BLINDERN 0315 OSLO, NORWAY E-mail: sam.roberts@ifikk.uio.no URL: http://samrroberts.net

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A STRONG REFLECTION PRINCIPLE

  • SAM ROBERTS

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