A fairly simple question: I've read in multiple sources that Godel proved that if we accept the axiom of constructibility in ZFC, then we can create an explicit formula that well-orders the real numbers. I tried searching for a paper or some other source that explains what this formula is, but I came up empty-handed. Can someone explain what this formula is, or perhaps point me to a resource that does?



V=L and a Well-Ordering of the Reals
The order is very easy. Under $V=L$, the set-theoretic universe is built according the hierarchy $(L\_\alpha \mid \alpha \in \mathrm{Ord})$, where $L\_0$ is empty, $L\_{\alpha+1}$ consists of all definable subsets of $L\_\alpha$, and $L\_\lambda$ is the union of all earlier $L\_\alpha$ when $\lambda$ is a limit ordinal. 


Since we can order the definitions used to go from $L\_\alpha$ to $L\_{\alpha+1}$, we obtain a definable well-ordering of the entire universe. Namely, $x$ is less than $y$ iff 


1. $x$ appears before $y$ in the hierarchy or
2. they appear at the same stage, but $x$ appears with an earlier definition than $y$.


If one analyzes the complexity of the resulting definition for real numbers, it has complexity $\Delta^1\_2$ in the descriptive set theoretic hierarchy. 


