Taking Reinhardt's Power Away

Richard Matthews

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arXiv · 2009.01127

Taking Reinhardt's Power Away

Richard Matthews

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Abstract

We study the notion of non-trivial elementary embeddings $j : V \rightarrow V$ 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 $V_{\textrm{crit}(j)}$ 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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Richard Matthews. 2020-09-02. Taking Reinhardt's Power Away. https://arxiv.org/abs/2009.01127

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