By Morse Anthony P.
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63 DEFINITIONAL SCHEMA. We accept as a definition each expression which can be obtained from “IPI = I(P)O’ by replacing I p by a march and ‘ ’ by an expression of class 5. 26 0. Language and Inference For example ‘(Ix + x’ + X”I = I ( x + x’ + x ” ) I ) ’ is among our definitions. 64 DEFINITIONAL SCHEMA. We accept as a definition each expression which can be obtained from ‘ (A1 CPBYY! = A1 cp(B)YUY) ’ by replacing ‘B’ by a march and ‘Al’ by an expression of class 6. I n trying to make sure that our definitions conform to the Appendix we now pick up some loose ends.
S is a subject of A if and only if s is such a verbless expression, whose terminal symbol is a binariate, that either A is s or A can be obtained from xyz by replacing x by s, ‘y’ by a verbal nexus, and ‘ 2 ’ by an expression. Clearly an expression can have at most one subject. 55 AGREEMENT. C is of order n if and only if C has a subject in which precisely n binariates appear. 56 D E F I N I T I O N A L S C H E M A . We accept as a definition each expression which can be obtained by replacing ‘ E ’ by a n expression of class 0, ‘A’ by a n expression of class 1 , ‘ V ’ by a n expression of class 2, and ‘sup’ by an expression of class 3 in any one of the following expressions : ‘ ( E x ;_u x_v x = EX(UXAVX))’ - ‘ (Ax ; _ux _vx = Ax(0 E _ux + vx)) - ’ ‘ ( V X ; -UX -VX E vX(0 E -UX A _VX)) ’ ‘ (sup x -vx = sup x ; ( x = x ) yx) ’.
9 Our symbols of type 9 are : ‘ @’, ‘ +’, ‘ ‘ 0,’. ‘ 0 2 ’ 9 ‘0 3 ’ ’ ‘ 04)’ ‘ 0 5 ’ 9 ‘ 0 6 ’ ~ . 1 1 Our symbols of type 11 are: ‘-’, ‘ 03’,‘ 06). 13 Our symbol of type 13is: ‘/’. ’, ‘*’, l-l-. ‘o’, . 1 7 Our symbol of type 17 is : ‘ 5 a . 19 Our symbol of type 19 is : ‘ #’. 31 AGREEMENTS. O A symbol is a binarian if and only if it is a symbol of some type. 1 Asymbol is a binariate ifand only if it is either ‘ x ’ or one of the primed symbols derived therefrom. is a nexw if and only if c is a n expression in which each symbol is a binarian.