How strong is a Reinhardt set over extensions of CZF?

2021/01/19 by Hanul Jeon, Jeon, Hanul
Computer Science · Mathematics · #03E55 #03E70 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2101.07455

openalex publication_date 2021/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the lower bound of the consistency strength of CZF with Full Separation Sep and a Reinhardt set, a constructive analogue of Reinhardt cardinals. We show that CZF+Sep with a Reinhardt set interprets ZF^- with a cofinal elementary embedding j\colon V\prec V. We also see that CZF+Sep with a Reinhardt set interprets ZF^- with a model of ZF+WA₀, the Wholeness axiom for bounded formulas.

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