  The Wholeness Axioms, proposed by Paul Corazza, axiomatize the existence of
an elementary embedding j:V-->V. Formalized by augmenting the usual language of
set theory with an additional unary function symbol j to represent the
embedding, they avoid the Kunen inconsistency by restricting the base theory
ZFC to the usual language of set theory. Thus, under the Wholeness Axioms one
cannot appeal to the Replacement Axiom in the language with j as Kunen does in
his famous inconsistency proof. Indeed, it is easy to see that the Wholeness
Axioms have a consistency strength strictly below the existence of an I_3
cardinal. In this paper, I prove that 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 WA_n are not all equivalent. Furthermore, the
theory ZFC+WA_0 is finitely axiomatizable.
