Download PDF by Morse Anthony P.: A Theory of Sets

By Morse Anthony P.

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O ( A : :B ) is the expression obtained from ‘ixy’ by replacing ‘2by A and ‘y’ by B. ( A :B ) is the expression obtained from ‘my’ by replacing ‘ x ’ by A ,1 and ‘y’ by B. 81. 30 0. 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.

71 A G R E E M E N T . S is a string if and only if S can be obtained from one of the expressions G X > , GXXI,,

A variable is indicial in a form if and only if it occurs therein more than once. 21 RULE. A variable is accepted in a form if and only if it occurs therein less than twice. Thus a variable is accepted in a form, as opposed to a formula, if and only if the variable is free in the form. 22 RULE. If A , B, and C are formulas with A different from B and B different from C, and ifB can be obtained from A by replacing a free and accepted variable of A by C, then : a is accepted in B if and only if a is accepted in A , and a is indicial in B if and only if a is indicial in A and does not appear in C.

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