A Theory of Sets - download pdf or read online
By Anthony P. Morse
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Additional resources for A Theory of Sets
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. Thus a variable is accepted in a form, as opposed to a formula, if and only if the variable is free in the form. On the other hand, a variable is indicial in a form if and only if it is not free therein. 22 RULE. If A, B, and C are formulas with A different from B and B different from C, and if B 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.
35 it uses - ‘((x E Ex gx) @x A V y(x E y)))’ as an axiom of classification. It also fails quite naturally in our view to answer some of the simplest questions about the interplay of logic and set theory. The last and less fundamental part of Chapter 0 is dominated by our Theory of Notation. Many notations in common use in present day xxix xxx Preface mathematics are automatically preserved. Among these are ‘(x + y’z + w)’ ‘Ix + y - z+ WJ’, and but not among these are ‘I xyz 1’ and ‘I x 1 y I z I ’.
22 0. Language and Inference Our theory of notation and subsequent mathematical definitions will make possible a unique interpretation of the two parades just mentioned as well as a host of others. AGREEMENT. A is of power n if and only if A is a nexus in which some symbol of type n appears and no symbol of type less than n appears. 34 For example, ‘<’, ‘<<’, ‘< n’, ‘C-E’ are of power 6. D E F I N I T I O N A L SCHEMA. 35 ‘((X A X’ A X”) ‘((X ((X A X’) A X”))’, A X’ A X” A X”’) ((X A X’ A X”) A X’”))’, etc.
A Theory of Sets by Anthony P. Morse