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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