# 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} }

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

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 23 REFERENCES

No Elementary Embedding From V into V Is Definable From Parameters

- Computer Science, Mathematics
- 1999

17