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- W2023186414 abstract "These systems are roughly natural number theory in, respectively, n th order function calculus, for all positive integers n . Each of these systems is expressed in the notation of the theory of types, having variables with type subscripts from 1 to n . Variables of type 1 stand for natural numbers, variables of type 2 stand for classes of natural numbers, etc. Primitive atomic wff's (well-formed formulas) of T n are those of number theory in variables of type 1, and of the following kind for n > 1: x i ϵ y i +1 . Other wff's are formed by truth functions and quantifiers in the usual manner. Quantification theory holds for all the variables of T n . T n has the axioms Z1 to Z9, which are, respectively, the nine axioms and axiom schemata for the system Z (natural number theory) on p. 371 of [1]. These axioms and axiom schemata contain only variables of type 1, except for the schemata Z2 and Z9, which are as follows: where ‘ F(x 1 )’ can be any wff of T n . Identity is primitive for variables of type 1; for variables of other types it is defined as follows:" @default.
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- W2023186414 date "1953-06-01" @default.
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- W2023186414 title "Some formal relative consistency proofs " @default.
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- W2023186414 doi "https://doi.org/10.2307/2268946" @default.
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