 Takeuti refers to (*) as the accessibility of \(\prec\). Note that this is a weaker property than the well-foundedness of \(\prec\) which refers to arbitrary sequences. There is nothing special about the case of PA since any ordinal analysis of a theory T in the literature can be made to fit this format. Thus epistemologically (*) is the fulcrum in any such consistency proof. Takeuti’s central idea (1987, 1975) was that we can carry out Gedankenexperimente (thought experiments) on concretely given (elementary) sequences to arrive at the insight that (*)  obtains.[16] 