The Wholeness Axioms and V=HOD

@article{Hamkins2001TheWA,
  title={The Wholeness Axioms and V=HOD},
  author={Joel David Hamkins},
  journal={Archive for Mathematical Logic},
  year={2001},
  volume={40},
  pages={1-8}
}
  • J. Hamkins
  • Published 13 February 1999
  • Economics, Philosophy
  • Archive for Mathematical Logic
Abstract. If the Wholeness Axiom wa $_0$ is itself consistent, then it is consistent with v=hod. A consequence of the proof is that the various Wholeness Axioms are not all equivalent. Additionally, the theory zfc+wa $_0$ is finitely axiomatizable. 
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References

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TLDR
One of the standard ways of postulating large cardinal axioms is to consider elementary embeddings, j, from the universe, V into some transitive submodel, M, and it is shown that whenever κ is measurable, there is such j and M .