By Morse Anthony P.
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We agree that C is primitive if and only if either C is a schemator, or C is ‘ = ’, or C is ‘ ( x _= y) ’, or C is such a definiendum that no definition raises a variant of C. Our primitive constants consist of our definor and our schemators. We agree that S is primal if and only if S is one of the expressions : ‘(XEY)’, cx’, ‘XI’, CXI,’, - ‘UX’) ‘U’XX”, - ‘vx’, (wx’, ‘v’x“’, ‘W’X”’, - cUIXXIXn’, - rVIxXlXW~, - etc. cWnXXIXW5, - 6 0. Language and Inference We agree S is schematic if and only if S can be obtained by replacing variables by variables in some primal expression in which a schemator appears.
49 DEFINITIONAL SCHEMA. We accept as a definition each expression which can be obtained from ‘ ( ( X *E 9) (x E 9 + A ZZ)) ’ by replacing ‘E’by a nexus different from ‘m’. 57. 50 AGREEMENTS. 1 ‘One’, ‘The’. Our expressions of class 1 are: ‘A’, ‘A’, ‘far R’, ‘large’, ‘small’, ‘big’, ‘alm # Mcp , ‘alm q’, ‘Alm ‘p’, ‘A1 cpB. 3 ‘Ad’, ‘C’. Our expressions of class 3 are: ‘sup’, ‘inf’, ‘ad’, ‘osc’. 4 Our expressions of class 4 are those expressions which are of either class 0 or class 1 or class 2 or class 3.
Our theory of notation and subsequent mathematical definitions will make possible a unique interpretation of the two parades just mentioned as well as a host of others. 34 AGREEMENT. A is of power n if and only if A is a nexus in which some symbol of type n appears and no symbol of type less than n appears. For example, are of power 6. 35 D E F I N I T I O N A L SCHEMA. We accept as a definition each expression which can be obtained by replacing ' A ' by an expression of odd power in any one of the expressions: '((X A X' A X " ) SZ ( ( X A X ' ) A X " ) ) ', ' ( ( X A X ' A X " A X m ) E ( ( X h X ' A X " ) AXm))', etc.
A Theory of Sets by Morse Anthony P.