Corpus ID: 219177403

# On the consistency of ZF with an elementary embedding from $V_{\lambda+2}$ into $V_{\lambda+2}$

@article{Schlutzenberg2020OnTC,
title={On the consistency of ZF with an elementary embedding from \$V_\{\lambda+2\}\$ into \$V_\{\lambda+2\}\$},
author={Farmer Schlutzenberg},
journal={arXiv: Logic},
year={2020}
}
• Farmer Schlutzenberg
• Published 2020
• Mathematics
• arXiv: Logic
• Recall that $I_{0,\lambda}$ is the assertion that $\lambda$ is a limit ordinal and there is an elementary embedding $j:L(V_{\lambda+1})\to L(V_{\lambda+1})$ with critical point ${<\lambda}$. This hypothesis is usually studied assuming ZFC holds in the full universe $V$, but we assume only ZF. We show, assuming ZF + $I_{0,\lambda}$, that there is a proper class transitive inner model $M$ containing $V_{\lambda+1}$ and modelling the theory \[ \mathrm{ZF}+I_{0,\lambda}+\text{there is an… CONTINUE READING

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