By Morse Anthony P.
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78 AGREEMENTS. O A is a string-link of C if and only if A is a link of C and there is such a subchain C‘ of C that A is not a link of C‘ and A is of the kind (FB) where F is a formula and B is a link of C’. I C is a string-chain if and only if each link of C is either a formula or a string-link ofC. 79 RULE. S is a string if and only if there is a string-chain ofwhich S is a link. 80 AGREEMENTS. O A is an indicial-schematic-linkof C if and only if A is a link of C and A is of the kind ( a ::B ) where a is such a variable and B is such a formula that there are a subchain C‘ of C, a variable a, a schematic expression S, and a formula B for which: A is not a link of C‘; a appears in S; ( a : : B )is a link ofC’; ( a ::B ) is a link of C’ ; B can be obtained from B by schematically replacing S by a formula.
23. 28, replacing the words ‘ is accepted ’ by ‘ does not appear ’. T o assess the consequences of this proposed simplification let us adopt the unordered summation notation ‘ C x E A ux’. - 0. Language and Inference 12 I t is then natural to expect that (EnE 4 n = 6 = E m E 4 m). Also it seems clear that ‘ E x E y x’ is a formula. Inasmuch as ‘ (Y AxY) ’ is a formula in which ‘y’ is free it seems inescapable that -+ ‘ ( x -+ A x x ) ’ is a formula, but not, we hope, a theorem. Thus, since ‘y’ is free in ‘ Z x E y x’ we feel compelled to admit that ‘Ex Ex x’ is also a formula.
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. 5 Our expression ofclass 5 is: ‘1’. 6 Our expression of class 6 is : ‘Al’. 51 AGREEMENT. A symbol is a notarian if and only if it is the initial symbol of some expression of some class. 52 A G R E E M E N T . A is a march if and only if some parade in which no binariate is adjacent to a binariate can be obtained from ‘ (p) ’ by replacing ‘p’ by A .