In this talk, I will give a previously known proof of Girard's $\Pi^1_2$-completeness theorem of dilators, whose proof is more or less similar to that of the Shoenfield absoluteness theorem. As an application, I will explain how to get an effective version of the Shoenfield absoluteness theorem. I will also briefly discuss the connection between (Homogeneous) Suslin sets and preptykes, and how it can hint at the notion of measurable $n$-ptykes.