# Abstract The paper presents a uniform way of obtaining by forcing descending sequences of the iterations of HOD and describes their structure. Among other things the following results are proved: **Theorem.** Any model $M$ of ZFC can be obtained by the transfinite iteration of HOD in some generic extension $N$ of $M$, i.e. $M=\left(\mathrm{HOD}^{\mathrm{On}}\right)^N$. **Theorem (ZFC).** For any ordinal $\alpha$ there is a complete Boolean algebra $B$ with a decreasing sequence of derivatives of length $\alpha$. Moreover some other results about ordinal definability are reproved using the introduced method. This method is a refinement of the classical method of coding introduced by McAloon in [[McAloon - Consistency results about ordinal definability]] and [[McAloon - On the sequence of models HODₙ]]. >[!note] Notation >A cardinal $\kappa$ is *critical* if $\kappa=\omega_{\kappa}$. The class of critical cardinals is denoter $\mathrm{K}$. **Definition 2.2.** We say that an ordered set $C$ is *homogeneous* iff for all $p, q$ in $C$ there exists an automorphism $\sigma$ of $C$ s.t. $\sigma(p)$ and $q$ are compatible. (This is now usually called [[Homogeneity|weakly homogeneous]])