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.

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.

The order is very easy. Under V=L, the set-theoretic universe is built according the hierarhcy L_alpha, 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 hiearchy 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.

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.