By Morse Anthony P.
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CONTENTS FOREWORDvii PREFACExxv 0. Language and Inference 1 Introduction 1 Replacement 1 Expressions 2 Rudiments 3 Schematic Replacement 6 Orienting Definitions 6 Free Variables and Formulas 7 Indicial and Accepted Variables 10 Rules of Inference ; Theorems 12 Initiation 12 Detachment 13 Substitution 13 Schematic Substitution 13 Indicial Substitution 13 Universalization 13 Theory of Notation 15 Demonstrations 27 Chains 29 1. Logic 33 Definitional Axioms for Logic 33 Axioms of Definition for Logic 34 Axioms for Logic 34 xxix xxx Contents 2.
2 A is an indicial-free-link of C if and only if A is a link of C and A is of the kind ( a ::B ) where a is such a variable and B is such a formula that there are a subchain C‘ of C, a variable /3, and a formula B for which: A is not a link of C’ ; ( a : : B )is a 1inkofC’; 31 Chains fi is free in B ; (fi:B ) is a link of C‘; B can be obtained from B by replacing fi by a formula in which a does not appear. : B ) is a link of C’; B can be obtained from B by replacing fi by a formula. 4 A is an indicial-start if and only if A is of the kind ( a :: F ) where F is a form and a is a variable which occurs in F more than once.
Theory of Notation 21 If A is the expression '(X A< then 'A<< X' A < < X" A < X'" A < < X"")' ' is of prime importance in A and the complicate of A is A<< '((XA
A Theory of Sets by Morse Anthony P.