Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

SECTIION Cl

INDIUCTIVE CARDINALSi

223

F. *3729 3.*al 20~4621.) F:. H p.):/3(~ 1 )*s m,,"a. ). sm1~"/3(-i l )*cSm"' a (4~)
F.(3). (4).)D F I Prop
It is on this proposition that the irrelevance of types in the consideration
of inductive cardinals depends.
*120-463. F::. a E NC.I):: (-y).yeN,=Cinduct. = (a +,0y)I.:.
~ C.'.(U + IVE p.: Sill, "a ep C.P '
[*120-462. *90-11]
*(120-47.:PeNCidc '.~~~ 1.(,1,c~,e~,~ ~
[*1 20'423-463]
Thus mathematical induction starting from 1 will apply to all inductive
cardinals except 0. Similar propositions can be similarly proved for 2, 3,....
*120-471. F: (3a). a E NC induct - ff0.fa.. (:3). / 8 NC induct.f( +,3~1)
Dem.
F.*120-423.
F: (ga) a a E NC induct - 00..fa.. (~/3). / f NC induct. a = / +0 1.fr.
[*13~195] -=-. (a/3) ~./3eNCinduct. f(3+01):DF.Prop
*120-472. F: (gca). a E NC induict - f0 - t'1.fa.
(~/). /3 E NC induct - ff0.f(/ +,~1).. (:y). y e NC induct.f(y +02)
Dent.
F. *1 20-471.
F: (,a). a e NC induct - f00 - iii fa.
(g/)*. 3 e NC induct. / +,~ 1 j 1.II'(13 +1).
*1 20-42.*110641]. (,/3). /3 NC induct - t,0.fI(3~ +, 1). (1)
L*I2047 1]. (y).,ye NC iiiduct *t'(y ~I +, 1).
[*11 0C43] E. (~_y)I y e NC inmd uct.f( 02) (2)
F. (1). (2). ) F I Prop
*120-473. F:. 1: EN,7induct-t6O 5.,. F+,rl): )
e N,C induct-f0. ).JT)ena.
F. *120-.11124. ) F: E NIC induct - ff0. ). 0 + 0 1 e NqC induct ff0 (2)
F:. Hp.D:l EN,C induct - ff0. b1.: 4 eN,Cinduct - ff0. 4.:).
F (3) *12047I (e E NNC induct - dc'0. ) F Prop
F. (3). *1 20-47 (.,C ndc -00F Prop