User blog comment:P進大好きbot/FGH beyond PTO(ZFC)/@comment-36957202-20190225125534/@comment-35470197-20190225215645

Its definition is the latter equation in 3.1 in Notation System. Namely, \(\Theta\) is the first entry of \(A_{L-1}\), and \(\Phi\) is the third entry. They are code arrays by the definition of a decreasing sequence array, and hence correspond to Turing machines. That is why the substitution \(\Phi(k,n)\) makes sense.