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A STRONG REFLECTION PRINCIPLE

Published online by Cambridge University Press:  01 November 2017

SAM ROBERTS
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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).

Keywords

03A0503E5503E6500A30set theoryreflection principleslarge cardinalsintrinsic justification
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 4 , December 2017 , pp. 651 - 662
Copyright
Copyright © Association for Symbolic Logic 2017 

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References

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