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Download A Theory of Sets by Anthony P. Morse PDF

By Anthony P. Morse

ISBN-10: 0080874274

ISBN-13: 9780080874272

ISBN-10: 0125079524

ISBN-13: 9780125079525

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Extra info for A Theory of Sets

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We shall soon learn that mathematical expressionals have no quotation marks in them. 0, but we feel this machinery of concatenation now and then considerably shortens explanations. We agree that c is a symbol if and only if c is a mark which is not a quotation mark. An expression is a linear array of symbols. As will be seen, quotation marks play a central role in this chapter. 0 into a contradiction. 0. It helps to notice, for example, that ‘ptq < r + s’ is an expression in which, of course, no quotation marks appear; on the other hand “p +q

No formula is an initial segment of a different formula. RULE. If A is a prefix, B is a suffix, and ( A B ) is a reducible formula, then some initial segment of B is a formula. 18 Remark. 8 of Appendix A. 14 0. 19 RULE. If a is indicial in A, then a is a variable and A is a formula; if a is accepted in A , then a is a variable and A is a formula. RULE. 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.

The individual constants are usually incidental. The expression ‘ ( p + q)’ has nothing to do with limits and the expression ‘(cx +A as x + a)’ has nothing to do with implication. 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 ‘(x = y)’, ‘x’, ‘XI’, ‘Xnr, ‘gx’, ,’,, ,’,‘ ‘g1xxt’, yXx1’, ‘ylxx”, ‘UnXX,X,,,,‘VnXX,Xn,,‘WRXXIXl17, - - - etc.

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A Theory of Sets by Anthony P. Morse

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