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PRELIMINARIES 1 Forms and functions 8 Operators and bound variables 14 Use of algebraic notation 23 Notation for twovalued truthtables 30 Modal logics 41 Scope of logical operators 47 Quantifiers 54 Functions from classes of classes to classes 97 Calculus of individuals 98 CALCULUS OF RELATIONS 100 Relationtorelation functions that are proper to the relational calculus 104 to relations 106 Functions from relations to classes 107 Identity and notions derived from identity 109 Representation of nonpropositional functions by their associ ated relations 113 Tables of symbols 57 An example of a firstorder functional calculus 58 Quantifiers in nonclassical logic 60 Firstorder functional calculus with identity 62 Quasidefinite descriptions 64 FUNCTIONAL CALCULI OF HIGHER ORDER THE THEORY OF TYPES 66 The theory of types 68 Explicit indication of type 70 Implicit indication of type 73 COMBINATORY LOGIC 74 The notation of combinatory logic 77 Example of a simple system of combinatory logic 79 Combinations and the theory of combinators 81 Lambdaconversion 84 Definitions of combinators as abstracts 87 Further extensions of combinatory logic 89 CALCULUS OF CLASSES 90 Variables abstracts and constants for classes 92 Operators corresponding to those of the functional calculus 93 Functions from classes to propositions 94 Functions from classes to classes 95 Some further important relations and classes 116 Relations of more than two terms 123 ARITHMETIC FORMALIZED AS AN INDEPENDENT DISCIPLINE 125 Formulation of the theory as an independent discipline 126 Recursive arithmetic 127 The ufunction 129 NUMBERS AS DEFINED WITHIN SYSTEMS OF LOGIC 130 Von Neumanns method of defining numbers 132 Arithmetic operations on natural numbers defined by means of the ancestral 133 Arithmetic operations on cardinal numbers 134 The definition of relationnumbers by ordinal similarity 137 Arithmetic operations upon relationnumbers 139 METAMATHEMATICS 141 Metamathematical variables and constants 143 Designations for classes of symbols and classes of entities 147 Designations for expressions 149 Substitution 152 Theoremhood and derivability 153 INDEX OF NAMES 157 Página de créditos