Taking Reinhardt's Power Away

2020/09/02 by Matthews, Richard
#03E25 #03E30 #03E55 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2009.01127

Abstract

We study the notion of non-trivial elementary embeddings j : V → V under the assumption that V satisfies ZFC without Power Set but with the Collection Scheme. We show that no such embedding can exist under the additional assumption that it is cofinal and either V_\textrmcrit(j) is a set or that the Dependent Choice Schemes holds. We then study failures of instances of collection in symmetric submodels of class forcings.

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