The ai are defined by transfinite recursion: we pick a0 in P arbitrary (this is possible, since P contains an upper bound for the empty set and is thus not empty) and for any other ordinal w we set aw = b({av : v < w}). Because the av are totally ordered, this is a well-founded definition.
The ai are defined by transfinite recursion we pick a0 in P arbitrary (this is possible since P contains an upper bound for the empty set and is thus not empty) and for any other ordinal w we set aw = b({av  v < w}) Because the av are totally ordered this is a well-founded definition