User blog comment:Boboris02/Algorithm for Generating LUCOs From TON Expressions + Intuitive Analysis/@comment-31580368-20180519034242/@comment-30118230-20180623121509

Sorry for the extremely late responce, I just haven't been very active.

No, large unrecursive ordinals are not connected to theories by default, but we can make a connecteion when considering minimal model heights in the constructable universe L.

It is correct that the first nonprojectible is the minimal model height of ZFC- and Z2, and that elements of the constructible hierarchy form models of ZFC- and Z2 at every nonprojectible ordinal'th element.