Why are we interested in definable wellordering of the reals? For instance, we have
- Con(ZFC) $\Rightarrow$ Con(ZFC + there is a $\Delta^1_2$-wellordering of $\mathbb{R}$),
- Con(ZFC + there is a measurable cardinal) $\Rightarrow$ Con(ZFC + there is a measurable cardinal+there is a $\Delta^1_3$-wellordering of $\mathbb{R}$).