230 Miss Wrinch, On the exponentiation of well-ordered series 



[-r4] D I- :: Hp . D :. SeCP"^ .D . S e p :v: T e p .Dj ■ 



SP'iTiv.'g^U.UeX.UP^S: 



D h :: Hp . D :. T^eX . D,- . SP'^V : S eC'P'^ : 



DiSep.v.Tep.Dr-^'^P'^T: 



D I- :: Hp . D :. (T = ?7(FeX . D,- . UP'W) - max (P'iyp . 

 SecTzD-.El max (P'^Yp . D . SP^ (max (P'^Yp) . 



max (P«) V epiv: i^'P« ^ = A . D . gT . .ST'-T . T e p : : 



D\-::lIl).D:.(T = U{Ve\. D,- . ?7P«F) - ^{P^p . 



D.aCP'^"p (1) 



h.(l).*205-193. DI-:.Hp.D:(7 = 0'(FeX.D,-- t^P'^F) 



-l'^(P«)V . D . ^(P«)'p u cr = ^(P'?)'p (2) 



h . *206-02 . D I- :. Hp . D : prec (P«)^X 



= ^' &( F 6 /,; . D . FP'^^ U) (3) 



h . (3) . :) h :. Hp . D : (7 = ^( Fe X . Dr ■ ^i"^'^^) 



- ^ (P«)'p . D . ^ (P«)'X = 1^ (P'-') Cp yj a) : 



|-.(2). Dh:.Hp.D:c7-f/(F6X.Dp.. f/^P^F) 



- rmJ (P«)> . D . prec (P<^)'X = nmJ (P''*)'p (4) 



I- . *-432 . D I- : Hp . D . i^ (P«)'X = A (5) 



h . (4) . (5) . *207-02 . D h : Hp . D . ^ (P^Yp = tl (P^)'^ 

 r44. h : Hp r42 . p = C'P^ nR{R\- d'PQ'X = PQ'X) .pel. 



D . T'p = tl (P«)'\ [*205-lS . *-433] 



*-45. h : . Hp r42 . p - C"P« n P (P p d'PQ'X = PQ'X) : 



D : a'PQ'X =G'Q. = .p = I'PQ'X 

 Dem. 



h :: Hp . D :. a'PQ'X = C'Q . D . PQ'X e G'P^ : 



Rep.D.a'R = a'PQ'X:: 



D I- :. Hp . D : a'PQ'X = C'Q . D . PQ'X = ^'p (1) 

 h :. Hp . D : /^ = t'PQ'X . D . PQ'X e (7'P« :. 



