By Morse Anthony P.

ISBN-10: 1114312681

ISBN-13: 9781114312685

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69 DEFINITIONAL SCHEMA. We accept as a definition each expression which can be obtained from by replacing ‘ I ’ by an expression of class 5 . 27 Demonstrations Remark. By added effort we could in the spirit of the foregoing give a much more sweeping theory of notation than the one herein given. We could, for example, so arrange things that expressions like ‘ (J”_UX . v x dx = J” (UX - . -VX) dx) ’ would automatically become theorems. Remark. 1, or a symbol fixed by the first formula in which it appears among those listed in the chapters which follow.

Remark. 1, or a symbol fixed by the first formula in which it appears among those listed in the chapters which follow. I n this connection we should like to point out that no symbol is ever fixed by an expression in which ‘ = ’ does nut appear. 70 A G R E E M E N T . 4 C is obtained from ‘Axy’ by replacing ‘ x ’ by t and ‘y’ by A . 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 is a su@x if and only if A is either a noun or an expression of the kind ( a B ) where a is an introductor and B is an expression. 12 AGREEMENT. fundamental. 13 RULE. introductor. 14 RULE. A formula is fundamental if and only if it is either a simple prefix or an expression of the kind (Act) where A is a simple prefix and ct is the initial symbol of A . 15 RULE. I f F is a strict formula devoid of schemators, and A is a form obtained from F by replacing variables by schematic expressions, then: F is a simple formula, every variable which appears in A also appears in F, a is free in F if and only if ci is free in A , and A can be obtained from F by replacing variables which do not appear in A by schematic expressions.

### A Theory of Sets by Morse Anthony P.

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