[FOM] Classification theory of abstract elementary classes by Shelah

[pax0 at seznam.cz]

Dear FOMers
there is a definition in the book from subject of this email which is not clear to me.

For ring M we define
dp:{u:u \subset M finite}-->the ordinals by
dp_M(u)=U{dp(w)+1:u\subset w and w is not included in the ideal of M which u generates}

What I do not understand is how induction is used here: i.e. how do we compute dp(w)
from the property on the r.h.s in { }.

Can someone help in some detail?
Jan Pax