Wikipedia contains the following information in the article "Admissible ordinal":
By a theorem of Sacks, the countable admissible ordinals are exactly those constructed in a manner similar to the Church-Kleene ordinal, but for Turing machines with oracles. [Reference: Friedman, Sy D. (1985), "Fine structure theory and its applications"]
I have found the referenced paper, but I cannot seem to find any reference to this theorem there.
Question: where can I find this theorem? What is its name (or identifier)?