User blog comment:Edwin Shade/The Grand List Of Transfinite Ordinals/@comment-30754445-20171130012046/@comment-24920136-20171130204750

You also get all of those if you include phi  in the closure functions. you could even in theory include klammersymbolen  (with the result being psi(0) = LVO) though none of it is nearly as strong as just  going up to the next cardinality. ( ps noone stops you from doing both!)