User blog comment:Edwin Shade/A Complete Analysis of Taranovsky's Notation/@comment-30118230-20180201150715/@comment-32876686-20180202232036

I know these may seem like novice questions, but in the past few days I've heard of new concepts and theories that I want to learn but haven't a clue where to start, so I'm asking questions.

1.) How do you find the proof-theoretic ordinal of nth-order arithmetic, and what, (in simple terms), does "nth-order arithmetic" even mean ? This is very similar to my earlier question of the meaning of \(\Pi^{\alpha}_{\beta}\), but I feel like the two are different, (might this be what LittlePeng9 was referring to when he said " this notation can mean two slightly different, but strongly related things, one in reference to set theory, one in reference to arithmetic." ?)

2.) Are there any webpages which give examples of such proof theoretic ordinal derivations in depth but which are at the same time accessible to someone who isn't experienced in rigorous, formal mathematics ?

Or if this is too much to ask for, are there any websites which at least talk about set theory without being so formal, but are still accurate ? (Something like Godel, Escher, Bach:An Eternal Golden Braid, that is.)

3.) Alemagno12's most recent blog post has got me asking, what does "Z2" and "Z3" mean ?

I know given my behavior you may feel inclined to decline these questions, but I know the answers I'll be able to help others when they have similar questions, and so you'd be helping many others learn as well.