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The Wholeness Axioms and V=HOD

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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Received: 16 February 1999 / Revised version: 1 June 1999

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Hamkins, J. The Wholeness Axioms and V=HOD. Arch Math Logic 40, 1–8 (2001). https://doi.org/10.1007/s001530050169

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