Pure Mathematics

Morse Anthony P.'s A Theory of Sets PDF

By Morse Anthony P.

ISBN-10: 1114312681

ISBN-13: 9781114312685

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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. 23 RULE. If A , B, and C are formulas with A different from B and B different from C, S is a schematic expression, some variable in S is indicial in A , and if B is obtained from A by schematically replacing S by C, then: a is indicial in B if and only if a is indicial in A , and a is accepted in B if and only if a is accepted in A and does not appear in C.

2 C is a free-chain if and only if C is a chain and each link of C is either a free-start or a free-link of C. 83 RULE. a is free in A if and only-if a is a variable, A is a n expression, and ( a A ) is a link of some free-chain. 84 AGREEMENTS. O A is a parenthetical-link of C if and only if A is a link of C and there are such a subchain C' of C and such a link B of C' that: A is not a link of C'; and A can be obtained from B by replacing a symbol which is not a parenthesis by a parenthetic expression.

28 were simplified in the way we momentarily have in mind, then we would be unable to interpret the formula ‘Ex E x x ’ . 28 to infer that ( E x E x x = Ey E xy). 24 INITIATION. Every formula asserted to be a definition or an axiom is a theorem. It should not be assumed that a formula is a definition just because it looks like one. Although always a theorem, a formula variant of a definition is seldom a definition. , is not a definition. Rules of Inference; Theorems 13 Definitions are more than mere shorthand devices.

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A Theory of Sets by Morse Anthony P.


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