  We study the influence of the existence of large cardinals on the existence
of wellorderings of power sets of infinite cardinals $\kappa$ with the property
that the collection of all initial segments of the wellordering is definable by
a $\Sigma_1$-formula with parameter $\kappa$. A short argument shows that the
existence of a measurable cardinal $\delta$ implies that such wellorderings do
not exist at $\delta$-inaccessible cardinals of cofinality not equal to
$\delta$ and their successors. In contrast, our main result shows that these
wellorderings exist at all other uncountable cardinals in the minimal model
containing a measurable cardinal. In addition, we show that measurability is
the smallest large cardinal property that interferes with the existence of such
wellorderings at uncountable cardinals and we generalize the above result to
the minimal model containing two measurable cardinals.
