Possible inconsistency related to embeddings $j: M\prec V$ In the paper

Vickers, J.; Welch, P. D., On elementary embeddings from an inner model to the universe, J. Symb. Log. 66, No. 3, 1090-1116 (2001). ZBL1025.03049.

it is stated to that if $Ord$ is Ramsey (I.e. there is a proper class $I\subseteq Ord$ of good indiscernibles), then there is a definable class $M$ and some $j: M\prec V$. But, according to Generalizations of the Kunen Inconsistency, there can be no $j: M\prec V$ for $M$ a definable class?
Does this mean that measurable cardinals are inconsistent, or is something else going on?
 A: There is no contradiction here.
Look at Theorem $2.3$:

Suppose $I\subseteq On$ witnesses $On$ is Ramsey. Then, definably
  over $\langle V,\in, I\rangle$, there is a transitive class $M$, and an elementary embedding $j :\langle M,\in\rangle\rightarrow\langle V,\in\rangle$ with $j \not= id$.

Note that $I$ is involved as a parameter in the definition of $M$ and $j$. But definability in the Generalizations paper means definability in $\langle V,\in\rangle$ alone.

Contrast this with the sentence

conversely, if $On$ is Ramsey, then such a $j, M$ are definable

from the abstract, where the dependence on $I$ is unstated. "Definability" is being used as a shorthand for "definability from witnesses to the relevant hypotheses." I personally dislike this and in my opinion the abstract is a bit unclear; that said, I understand the impulse to abbreviate results in the abstract, and the corresponding theorem in the body of the paper is clearly stated. I think the takeaway is that results in the abstract or introduction should never be completely trusted (especially when taken at face value they imply something glorious which isn't itself stated).
