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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A is strict if and only if A is a formula and not a variable. A G R E E M E N T . F is fundamental if and only if F is either a schematic form, or a strict formula devoid of schemators from which some form can be obtained by replacing variables by schematic expressions. 6 ‘(x + t)’, ‘u’xy’, ‘ A yx’, ‘x’, ‘ A xx’, ‘ A x EX’, ‘ A X ~ ’ ,and ‘(x+x)’, the first three are fundamental formulas and the last five are formulas which are not fundamental. A G R E E M E N T . tl is an introductor if and only if tl is a constant which is the initial symbol of some definiendum.

For example, (‘sin’ ‘x’) is ‘sin x’. Remark. We suppose herein that C is (‘x’‘x’‘x’). 0, it is easy to see that C is ‘xxx’. 12 0. Language and Inference On p. 2 we agreed that quotation marks are not among our symbols. 0 alone a contradiction would arise as follows. We also suppose A is ‘ x ’ ; A’ is ‘x’ ‘ x ’ ; B is ‘x’ ‘ x ’ ; B’ is ‘x’. 0 we have on the one hand C is (AA’) and on the other C is (BB’). But (AA’) is ‘xx’ ‘x’ and (BB’) is ‘x’ ‘xx’. However, ‘xx’ ‘x’ is not the same as ‘ x ’ ‘xx’, nor is either the same as ‘xxx’.

9 AGREEMENTS. O (AA’)is the expression obtained from ‘xy’by replacing ‘x’by A and ‘y‘ by A’. 1 (AA’A”)is ((AA’)A”). 2 (AA’A’’A’’’)is ((AA’A’’)A”’). etc. In other words, ( A B ) is the concatenation of A and B. For example, (‘sin’ ‘x’) is ‘sin x’. Remark. We suppose herein that C is (‘x’‘x’‘x’). 0, it is easy to see that C is ‘xxx’. 12 0. Language and Inference On p. 2 we agreed that quotation marks are not among our symbols. 0 alone a contradiction would arise as follows. We also suppose A is ‘ x ’ ; A’ is ‘x’ ‘ x ’ ; B is ‘x’ ‘ x ’ ; B’ is ‘x’.

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A Theory of Sets by Anthony P. Morse


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