User blog comment:DrCeasium/new hyperfactorial array notation/@comment-5529393-20130416153852/@comment-5529393-20130416193300

Up-arrows don't really work with transfinite ordinals (although people keep using them anyway), but yes, it does appear that your linear arrays go up to phi(omega, 0). Congratulations! I'll examine how far your extensions go.

I would still like an answer to my previous question:  What do you do when the first entry is an array? e.g. 3! [[4,2],1,2]